In the 80s, the two great 16/32-bit desktop CPU architectures were the x86, used in the IBM PC and compatibles, and the 68000, used in the Amiga, Atari ST, Macintosh, early UNIX workstations and really most things that were not trying to run MS-DOS.
With the rapid growth of MS-DOS, there inevitably developed an interest in running it on 68000 machines anyway, either by providing an x86 second processor or by software emulation. (Both of those solutions were tried on the Amiga, for example.)
One fundamental problem with this is that the x86 is little endian and the 68k is big endian, which would cause chaos every time you tried to transfer binary data between the two.
It occurs to me to wonder whether you could add any kind of glue logic to make the 68k run little endian, e.g. by swapping byte lanes in the data bus.
But it seems to me there is going to be a fundamental problem with that. You could swap the two bytes in a 16-bit transfer. But the 68k transfers 32-bit numbers as a pair of 16-bit chunks, in sequence. The glue logic would have no way of knowing whether a pair of 16-bit transfers, one after the other, were meant to be the two halves of a 32-bit word (in which case they would need to be swapped) or separate words (in which case they would need to be kept as is). I'm guessing that's the reason I never heard of anyone making the 68k run little endian.
(The 68020, with its 32-bit data bus, would be an easier proposition. But by the time that chip was widely used, I think people had mostly given up on running MS-DOS on anything other than fully IBM-compatible hardware.)
Am I missing anything, or is that indeed why no one ever did run the 68k little endian?