It it well-known that the existence of one-way functions is necessary and sufficient for much of cryptography (digital signatures, pseudorandom generators, private-key encryption, etc.). My question is: What are the complexity-theoretic consequences of the existence of one-way functions? For example, OWFs imply that $\mathsf{NP}\ne\mathsf{P}$, $\mathsf{BPP}=\mathsf{P}$, and $\mathsf{CZK}=\mathsf{IP}$. Are there other known consequences? In particular, do OWFs imply that the polynomial hierarchy is infinite?
I'm hoping to better understand the relationship between worst-case and average-case hardness. I'm also interested in results going the other way (i.e. complexity-theoretic results that would imply OWFs).