But it works, for the same reason that audio engineers use 64-bit signal pipelines inside their DAW even though nearly all output equipment (and much input equipment) is 16-bit which is already at the limit of human perception.

If you have a 16-bit signal path, then every device on the signal path gets 16 bits of input and 16-bits of output. So every device in the path rounds to the nearest 16-bit value, which has an error of +/- 0.5 per device.

However if you do a lot of those back to back they accumulate. If you have 32 steps in your signal path and each is +/- 0.5 then the total is +/- 16. Ideally some of them will cancel out, but in the worst case it's actually off by 16. "off by 16" is equivalent to "off by lg2(16)=4 bits". So now you don't have 16-bit audio, you have 12-bit audio, because 4 of the bits are junk. And 12-bit audio is no longer outside the limit of human perception.

Instead if you do all the math at 64-bit you still have 4 bits of error but they're way over in bits 60-64 where nobody can ever hear them. Then you chop down to 16-bit at the very end and the quality is better. You can have a suuuuuuuper long signal path that accumulates 16 or 32 or 48 bits of error and nobody notices because you still have 16 good bits.

tl;dr rounding errors accumulate inside the encoder