Actually the Bitcoin wiki says bitcoin is compatible and will be used for and by modern banks.
Like it or not, it actually makes sense to use modern banks with bitcoin for the same reasons we use them with fiat. Lending is a huge and important part of the economy, and some users really don't want to worry about security. You can "be your own bank" with USD Cash but most let banks worry about keeping their money safe. This will almost assuredly continue.
Modern banks aint really banks, theyre just like Bitcoin exchanger platforms that goes in the name of modern banks. Real banks are the ones controlled by a countrys central bank, so anything else apart from that is not a real bank.