As mentioned by the others above, I don't see this happening in a trustless, decentralized setting. Any alt that would go this route would likely die of hyper-inflation, due to everyone trying to gain as much leverage as possible. Any protocol layer on top of Bitcoin would go bust as soon as enough people are trying to run for the door -- ie. on-chain settlement.
However in a way it's already (potentially) happening in the form of BTC futures, leveraged trading and arguably USDT. All of which are run by central, more or less trusted entities, however.
Sorry of this will break the chain of discussion but I had unanswered questions from previous threads that seemed to be about LN grievances, citing nodes as banks charging interest - something I couldn't find reference to.
Is this possibility OP discusses (and achow clarifies) where this idea of interest bearing loans come from?
I guess "nodes as banks charging interest" refers to LN transaction fees? Seems like a weird comparison though, as we already have a similar thing going on in the form of miner fees for on-chain transactions. Difference being, that in the case of LN nodes the fee market is much more favorable for people trying to transact money.