LC didn't start it, it followed a number of other generally similar "peer-to-peer" lending services (Prosper.com is the first US one I'm aware of -- about two years before LC -- and ISTR there was at least one UK one about the same time as Prosper).
And banks don't get into it because it would involve risking the resources on a new business whose success outcome would be driving customers to account choices where the bank keeps less of the income from lending.
If the quasi-peer-to-peer-model becomes popular, banks will grudgingly get into it because then the choice will be between giving up all of the money to competitors rather than giving some of it up to investors in quasi-P2P loans, but they'd rather not stamp their imprimatur on the model while it still might fail to become a significant factor in how people invest and seek loans.
https://www.wellsfargo.com/personal_credit/
http://www.eloan.com/personal-loans
https://www.discover.com/personal-loans/
My guess is that they constitute such a small revenue stream for the banks, that banks skip on marketing and execution.
But would be the bank's role in a peer-to-peer transaction? Pure servicer?