Seems reasonable to build a cryptocurrency around this. The network could pay the cryptocurrency out to users dedicating resources. Have you thought about that?
Freenet's approach works well for things like group chat, where temporary inconsistency is mostly just an irritation, but for a cryptocurrency it is fatal.
I'm not saying you couldn't build a cryptocurrency on Freenet, but you'd still need a solution to that problem.
Currently it appears centralized, but in principle it'd be pretty easy to shift it to a web of trust instead, and hosts can choose what they allow and how much they value it.
(zero-knowledge proofs seem probably rather important to adopt tho, as right now it'll tie you to a stable pseudonym)