Chomsky did the opposite of what you're saying. He didn't ignore spoken language. He said that human vocalization is independent of language, and that the way our brains can manipulate and use sound (a cognitive capability, not specifically an aural one) is the fundamental differentiator that allows us to make compound ideas, and our specific use of language is a byproduct.

Example: a programming language's capability to produce complex software does not come from some inherent quality of language. It comes from binary. 0's and 1's, representing basic logic, and that being built on top of with an abstract "tool" called a language. If the binary logic didn't work, the language wouldn't do anything.

A dolphin can make sounds, and technically has a language, but they can't manipulate or recursively compound concepts (as far as we can tell) in order to create modified ideas. If they could, they probably would have come up with vastly more advanced fishing methods than the (admittedly novel) ones they have now.