For what it's worth, I wonder the same thing and think it's not as obvious as others suggest. e.g. if you have an autoencoder for a one-hot encoding, you're essentially learning a pair of nonlinear maps that approximately invert each other, and that map some high dimensional space to a low one. You could imagine that it could instead learn something like a dense bit packing with a QAM gray code[0]. In a one-hot encoding the dot product for similar tokens is zero, so your transformations can't be learning to preserve it.

Somewhat naively, I might speculate that for e.g. sequence prediction, even if you had some efficient packing of space like that to try to maximally separate individual tokens, it's still advantageous to learn an encoding so that synonyms are clustered so that if there is an error, it doesn't cause mispredictions for the rest of the sequence.

I suppose then the point is that the structure exists in the latent space of language itself, and your coordinate maps pull it back to your naive encoding rather than preserving a structure that exists a priori on the naive encoding. i.e. you can't do dot products on the two spaces and expect them to be related. You need to map forward into latent space and do the dot product there, and that defines a (nonlinear) measure of similarity on your original space. Then the question is why latent space has geometry, and there I guess the point is it's not maximally information dense, so the geometry exists in the redundancy. So perhaps it is obvious after all!

[0] https://en.wikipedia.org/wiki/File:16QAM_Gray_Coded.svg