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Compared to its main rival from Sega, the Super Nintendo has a weaker CPU but a more powerful graphics chip.

According to http://web.archive.org/web/20080505070423/http://www.eidolons-inn.net/tiki-index.php?page=SegaBase+Genesis

The system as originally designed was way too expensive to be produced in a version affordable for the average consumer, let alone cost-effective for Nintendo. On top of that, project leader Masayuki Uemura was unable to meet Yamauchi's demand that the new box be back-compatible with the NES. The back-compatability feature was eventually abandoned; however, that only saved about US$75 on the anticipated end-user price tag. The chief culprit of the cost was, of course, the all-new graphics and sound processing suite upon which Yamauchi insisted. Designed in anticipation of the coming multimedia boom, it drove up the cost of the system so much that Nintendo was again forced to cut costs elsewhere or scrap it and risk being left behind. The problem was eventually solved by installing a slower CPU - a Motorola-based WDC65816 CPU - instead of the faster 10 Mhz MC68000 that Uemura originally intended. This meant that the new box would not be that much faster than the NES itself, so a math coprocessor (as cheap as Nintendo could cobble together) was thrown in to ease the processing strain a bit.

Okay, I'm not surprised they contemplated making the machine backward-compatible. I could imagine that motivating the choice of a 6502-derived CPU. I could imagine the backward compatibility feature being eventually dropped to save cost, and someone deciding it wasn't worth redesigning with a different CPU at that late stage.

But I am very surprised by the claim that an originally planned 68000 was dropped for cost reasons, simply because by the end of the eighties, the 68000 only cost a few dollars anyway. E.g. Byte, December 1988, advertises it for $9.95, and that's retail price in quantity one; in quantities of millions, the unit price would've been considerably less. (It doesn't give a price for the 65816, but does advertise the 65C02 for $7.95.) The data bus would be sixteen bits either way, so the impact on system cost would seem to be essentially zero.

Did Nintendo really change their mind about using the 68000? If so, how does this square with that CPU being so cheap even two years before the launch of the new console?

Did Nintendo really change their mind about using the 68000?

Hard to say, as these decisions where never public.

If so, how does this square with that CPU being so cheap even two years before the launch of the new console?

Maybe because the price of the CPU drops to almost zero when using the 65816 as IP. After all, they didn't use the stock CPU, but had their own chip done. The 5A22 was custom made for the SNES and integrated several additional components that would have been external to the 68k. Having one simple chip instead of a spacious 68k plus external logic is a great cost saver - especially when planing for a large production. Being a more simple CPU it also saved on chips space and thus again on cost.

While contemporary sales prices are always a good first step, they also need to apply to for the situation in question to become more than a hint.

Addendum:

The data bus would be sixteen bits either way, so the impact on system cost would seem to be essentially zero.

As far as I read it, it implies that the 65816 has a 16 bit data bus, which is not true (*1). The 65816 got only 8 data lines - reducing system cost a bit further.

*1 - It's a common misconception to think of the 65816 as a clean 16 bit CPU. It's rather an 8 bit 6502 with some 16 bit mode (switching between 8 and 16 bit data/register size at will) and a banked addressing system added. For most operations it'll be not faster than a 6502 at the same clock speed. The only real advantage (beside build in banking) is the possible use of 16 bit index registers allowing easy pointer handling within a 64 KiB bank. Quite handy for high level languages. The caveat is already in the name: 65-eight/sixteen.