It seems to me like, if you took a credit union, and then stripped out all the junk that isn't actually savings or loan - so free checking accounts, debit cards, ATM networks, branch locations & most the services offered therein, FDIC insurance, etc etc - how would that compare to Lending Club?

The biggest remaining difference would be the "peer to peer" bit itself. Which feels like a good thing to drop to me. From a purely financial perspective, the "you choose who to loan to" just feels like a way to introduce economic inefficiencies: The loan facilitator doesn't have a whole lot on the line, so they're poorly incentivized to do their due diligence on each loan. And the lender doesn't have direct access to the borrower, so they aren't able to do so in the first place. Nor, being non-bankers, are they likely to have the expertise to do a great job of it even if they could.

The more I think about it, the more peer-to-peer lending, at least as I understand it, sounds like CDOs in tie-dyed T-shirts.