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For the same reason nine women can't make a baby in one month.

The spells are full of components that simply can't be divided or done in parallel: each step requires a certain amount of time to complete and have to be done in a certain order.

Adding more resources can't make the steps go any faster, and more people may even cause it to take longer(which happens often in the world of software).

"If it takes an orchestra with 40 members 60 minutes to complete Beethoven's Ninth, how long will it take an orchestra with 60 members to complete the piece?"

Anyone vaguely familiar with how music works in even the most abstract sense should understand how absurd that question sounds, especially to a musician. Perhaps the question of adding more mages to speed up a ritual is equally absurd to a magician?

Rituals, like musical pieces, have a set tempo and duration to them. The tempo of the ritual may be altered, but not by adding or removing mages. Instead, additional mages might be added for a different reason altogether.

Taking again from musical practice, there is a thing that wind instruments will do called staggered breathing. When there is a particularly long note to be held, or when it is difficult to find a place to breathe without disrupting the rhythm, musicians will stagger when they breathe to make sure they don't breathe at the same time. If done well, the result is that no one hears any of them breathe, and the note and rhythm are never broken.

Perhaps your magicians make use of a similar staggered technique, where the additional participants are to ensure that the performance of the ritual is never broken, even if it would otherwise require an astounding and inhuman display of endurance.

For much the same reason that nine pregnant women together are not going to bear a child in one month.

The speed of a ritual is not proportional to the amount of mana you put in. In cooking terms, mana is an ingredient, not the fire. In more scientific terms, mana is not a form of energy - you don't measure it in joules - but a field, measured in thaums.

So adding more people or magic materials to a spell is akin to adding more dough to a pizza. It will feed more people, but it will not cause the pizza to be ready faster; Might even take more time to get it ready.

If you want to accelerate a spell, change not the materials, but the setting. Go to a volcano for fire spells, or cast lunar-related spells under a full Moon.

If a ritual takes 30 minutes then it's going to take 30 minutes if one person does it or a hundred people.

If 100 people recite, for example, the Lord's Prayer, they won't recite it any faster than one person.

It's like a water hose. There is a maximum volume of water that will flow through the hose, regardless of how large you make the tank it is attached to. In this scenario your primary caster is the end of the hose and the secondary casters are adding water to the tank.

More power requires more control of said power.

These rituals are already taxing on an individual, adding more people for more power only increases the pool of power available. The primary caster acts like the control unit and may or may not actually contribute power to the spell at this point. There can't be multiple people controlling the spell because they might step on each others toes and create feedback. Therefore, the spell can only be cast at the speed of the person shaping it no matter how much power is required.

The above examples are great, and true, but here's an alternative way of thinking of it specifically related to power.

You make a device that broadcasts radio, and the device required 1 AA battery to run. A second generation of the device has more features, and requires 2 AA batteries to provide the necessary power (amperage) for the device to operate. It would not, however, play the radio broadcast faster. In fact, if you took the first radio and added a battery, it would still consume the same power, meaning you'd have doubled the reserve of power available (proper wiring permitted, and in an ideal environment), but it would still only perform the function for which it was intended.

... the time frame of a ritual stays the same regardless of how many
casters there are. Why would this be the case?

Because in any magic system that is studied and applied, there is always the same problem, for the measure of Orgone there is an equal and opposite measure that counteracts that power.

Adding more practitioners simply makes the "Shadow Orgone" increase in power in a way that's proportional - and creates forces of chaos thus preventing progress. Since no shared psychic-mind has been succesfully created for the length of time necessary to cast a spell, yet, then only a single mind will be able to steadily work it.

Until the lost "Legion Spell" is found, that enables all minds to act as one.

That's why magical practice is essentially a solitary thing - even if it's practitioners are team-players and sociable people.

The different mages perform different and concurrent parts of the spell, which are all needed together to make the spell effective.

Think of it like two pillars and a beam. The beam holds the pillars and the pillars support the beam. They can only work together, having one less will make the whole ensemble useless.

If you need a flame at 300 ºC during an hour to cook a meal, a flame at 9,000 ºC won't cook it in 2 minutes.

An increase of heat (or power, mana, etc) doesn't necessarily increase the speed of the process.

Conduct a ritual isn't something that can be made in parallel, so it could be divided into small parts for each mage to cast.

It's like drawing, several artists (usually) can't work together in the same draw, their creative ideas are just different. Or like doctors, a surgeon can perform an operation in 4 hours, but 20 surgeons won't finish it in 12 minutes, even more, so many people will commit mistakes.

Spells and rituals are things that must be made in sequence, you can't just add more mages to divide the work. Each mage must perform a specific part of the ritual, so if a ritual was made to require 4 mages (one to channel the power, another to give it form, other to cast it and a last to supervise everything) you can't use 8 mages, there aren't enough jobs (or "magician slots") to perform, and these works can't be performed by several ritualists at the same time.

Even more, maybe magic is like a painting. Paint a wall can require a few hours to let it dry, several painters won't speed up the drying process. Mana or orgone needs time to acquire the shape of the spell, and that time can't speed up... not without suffering risk...

You answered your own question. There is one Primary caster and other subsidiary casters. One caster pulling on too much 'Orgone' can burn themselves out, so they evenly distribute their loads among other secondary casters.

However, the primary caster, who initiated the spell, is still the 'conduit' which pumps Orgone into the spell and powers it. The others are just ensuring that he has something to pump.

Therefore, the speed of casting will be determined by the power of the primary caster, and not by the number of casters working on the spell: Adding more casters (I'll call the secondary casters gatherers) will only reduce the load on each individual gatherer.

There's a limit to the flow of Orgone into a spell. A certain amount of Orgone is needed for a given spell to work. Orgone flowing through an individual is taxing work, and can exhaust individual spellcasters. However, working together, multiple spellcasters can divide the flow amongst them

The Orgone comes from a certain place in the astral plane, and has to travel to the site of the spell.

As a physical analogy, consider the spell "bring water". If I am on an island in a lake, a single caster can typically generate a small wave 1 metre tall bringing water from 10 metres out. Multiple casters can generate a wave that engulfs the island bringing water from 500 metres out. This requires more effort and (because the water comes from further out) it also requires more time.

It is possible to form a pond of water into a wave and magically cause it to roll over dry land carrying objects on top of it but this requires not only great power but also great skill. There is a legend of a Great One who can actually surf across land on a magical wave of their own creation.

Now consider these physical analogies involving water, and imagine that this is how the orgone flows to the site of the spell to be casted. For casting at a distance, the orgone may move directly from its resting place to the site of the spell or alternatively have to gather itself toward the caster then jet out towards the site of the spell. Clearly there will be a finite time for the orgone to travel there.

Orgone tends to collect in certain magical places such as caves and tends to evaporate in the city. There is a huge reservoir of it on the moon.

Now this leads to a problem: magical power without knowledge, wisdom, and good intent can be a dangerous thing. A powerful but unskilled individual is unlikely to do any damage, but a group of reckless young spellcasters can wreak havoc when they work together to wield powerful magic. They may for example send a tsunami of orgone toward a slowly approaching foe such as an army of trolls, only for it to backfire and engulf a village. For a sufficiently large spell there may even be time after the spell is cast to run and inform the villagers to evacuate before the spell hits.

Consider: the size of a symphony doesn't increase the speed of the piece. It can, however, make the piece more moving and effective.

Spells are a creative work.

The most difficult and time consuming part of creating a spell is thinking through how it is designed, how it's shape will affect the world.

A complex ritual would require the primary caster to think through an enormously complicated problem, like solving a 10x10 rubix cube in your mind. The extra casters can help provide more power, and more energy, but they can't make the spell any simpler.

Because only the primary caster is actually casting the spell in question.

All the assistant casters are casting a different spell: Supply Orgone to other caster

Because each mage has a particular magical "frequency" similar to radio waves. When multiple mages attempt the spell their magical "frequencies" cancel each other out.

Several answers already express what I want to say, I am just trying to give them additional conceptual background (they explain on examples, I will try to formulate a principle).

In order for a collectively cast spell to work at all, participants must draw from the same "direction" (not actual physical direction, but in some transcendental sense) of the power source. The more different their "directions of approaching the source" are, the more significantly does the result weaken. As an extreme example - if two mages draw from opposite sides, the result will be just weakening for both, without any positive outcome.

Now the nature of this "direction" is such that for several participants to find coinciding direction, they must overcome differences between each other, become less individual and more parts of a whole. The more mages are there to participate, the more difficult is it to achieve this goal. As the number of participants increases, inevitable individual differences that they simply cannot give up without ceasing to be themselves each become more and more apparent, thus reducing the effect of collective efforts.

for the same reason that

adding manpower to a late software project makes it later

from The Mythical Man-Month

It's a well know fact that magic and computer science are very similar.

From this you can simply replace mention to computer sciences in the overused quotes of The Mythical Man-Moth with spellcasting ones.

Here are a few:

Men and months are interchangeable commodities only when a task can be partitioned among many workers with no communication among them. This is true of reaping wheat or picking cotton; it is not even approximately true of spellcasting.

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Einstein repeatedly argued that there must be simplified explanations of nature, because God is not capricious or arbitrary. No such faith comforts the mage.

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I believe that large rituals suffer management problems different in kind from small ones, due to division of labor. I believe the critical need to be the preservation of the conceptual integrity of the product itself.