There is no guarantee that the Kolmogorov complexity of any interesting system will fit inside the rational parts of our heads. There pretty much is a guarantee that we will not be able to fully understand our own brains, using our brains; the part of our brain that can understand things is just dwarfed by the size of the rest of it. (We really do quite a lot with not very many free neurons.) Even if there is a generative theory that can explain human speech in less bits than a direct lookup table, there's no guarantee we can find it, and the null hypothesis must be that we won't because there is no such theory.

We should look for it, but we should not expect to find it.