I 100% agree with everything you said, I just wanted to make this point even more forcefully:

> Saying nature is mathematical is just saying that nature is consistent in the laws it follows.

It's more like "wherever nature isn't mathematical, we don't think about it as being mathematical", so saying "nature is mathematical" is very strongly tautological.

It's the same kind of situation as "why is everything linear?", or "why is everything an oscillator". The answer is more like "the things that aren't can't be easily described mathematically, and so we don't. What shakes out is mostly linear or quadratic (oscillators)".