I think very probably they will continue to exist.

Today their three main functions are:

1 - “we keep your money ‘safe’”

2 - issuing loans

3 - money creation via fractional reserves

Even if we assume that fractional reserve banking becomes impossible after people become unwilling to accept “a promise that can be redeemed for bitcoin later” (whatever form that ends up taking) rather than actual bitcoin, and even if we assume a massive shift in public mind-state such that everyone becomes comfortable holding their own money rather than trusting it to an institution (which I think is unlikely, at least until the wrench attack problem is solved), I think the loan-issuance need will still be met by something resembling a bank.

Obviously de-fi enables the possibility of overcollateralized loans without needing to ask anybody’s permission and without having to convince anyone that the loan is a good idea, but a bank makes it possible to take out a loan to get started with something - go to school, start a business, buy a house - without having anything to work with other than a hypothetical ability to earn money and a promise to pay it back. The bank has mechanisms to estimate the likelihood of that outcome, set an interest rate that makes it worth their while to take the risk, and direct connections to real-world enforcement mechanisms to prevent the borrower from just taking the money and running. If you remove the entity that is capable of establishing the connection between default and real-world consequences, “starter loans” become impossible.

So I think purpose #3 will be gone, purpose #1 will be diminished but not gone, and purpose #2 will keep them in existence and profitable.