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The Amiga 1000 came out in July 1985. This was an era in which personal computers were designed by their manufacturers to meet a unique set of bespoke requirements. For example, some computers came with advanced hardware for sound (for the time), while others had very primitive support for a "beeper".

It seems reasonable to conclude that personal computer buyers of this era tended to choose a system that focused on the hardware/software features that they felt were important for their own "use cases". Again, using the example of built-in audio support, a musician would be inclined toward a machine with more advanced audio capabilities. So would a gamer.

My question is what sort of use cases in 1985 led buyers toward purchasing an Amiga, and why would it be a better choice for those particular use cases than the PC, Macintosh, or Atari ST?

It was like a cheaper yet color Macintosh with a command line interface available. Stereo sound, better graphics, multi-process -- everything but sustained, intelligent marketing. (Initial marketing was good, but it was like they spent all their marketing money up front and expected momentum to carry them from that point.) I'm writing from an American viewpoint -- other countries weren't stuck in a mindset limited to PC or Mac. I like to say it offered more in 1985 than Windows 95 would a decade later.

The Atari ST won the high end music market with its standard MIDI interface. Unlike the Mac and PC, it could compete with the Amiga on price.

PC and Mac had much better business software support, and other high end programs such as AutoCAD pretty much ignored the Amiga and ST.

Probably the most well-known high-end Amiga software/hardware product was the Video Toaster from NewTek in 1987. It needed an Amiga 2000, which was a PC-looking machine with bus slots. It was a very popular video rendering system, and the graphics for the first couple of seasons of Babylon Five were produced with the Video Toaster and Amiga.

It was the only 16-bit computer with more than simplistic memory-mapped video hardware, with sprites reminiscent of the gaming-oriented 6502 processor color home computers (Atari 2600 and upwards and Commodore 64) but scaled upwards and separate "blitting" processing that could do the equivalent of sprites on bitmaps but with hardware acceleration. It had actual serious multitasking/processing. Compared to the state of technology, it was a very solid move forward from home computers to larger processing power and matching operating systems. "Personal computers", in contrast, highlighted the "business" angle and you'd see them advertised more likely with snapshots of spreadsheets than games.

It's possible that the high pricing of color monitors with reasonable resolution confined affordable reasonably ergonomic "computing" to monochrome displays, leaving color personal computers stuck with the display parameters of color TV sets which they strove to be compatible with.

The Macintosh with its built-in screen kept with monochrome (and CPU-manipulated bitmaps) for a long time, too.

So the Amiga was pretty much square where the technological advances would position the progress of home computers and in a space, for whatever reason, without serious contenders. But for whatever reason, also without serious perspectives. It took some time before acceleration became a thing on PCs, and even then, its "sprite" support never grew beyond a hardware cursor. Instead blitting and later triangle shading and other stuff you'd expect GL to deliver became a thing and eventually got good enough to kill off Silicone Graphics Workstations, at one time the epitome of heavy-duty graphics processing (rather than game-based graphics which had a different focus).