Don't forget about all the non-mining full nodes that would avoid having to carry the extra burden. Miners are getting financially rewarded for it, so it's much less of a problem for them.
The thing about Bitcoin is that it's in no way tied to a particular P2P network.
Back in ancient times, there was a P2P filesharing network called "Mojo Nation" that attempted to use market based resource allocation for bandwidth, storage, and content indexing.
It didn't really work out for several reasons, but it's probably worth dusting off, fixing its price discovery problems, and repurposing for Bitcoin.