There's always going to be trust issues when it comes to peer-to-peer lending, crypto will enable more capabilities and make it easier for people to lend to each other, but trust (underwriting, in a sense) and legal remedies will be essential for a long while to help make sure people will actually pay back their bills. Putting banking power in the hands of the populace makes this a lot easier to validate and process though. It'll happen, but it'll probably take a few decades.

(That said, this whole Bitcoin explosion happened faster and more suddenly than I ever expected.)