Not yet. There were several threads in the forum talking about banks and remittance companies getting their hands into blockchain research. They ain't disappearing anytime soon.
Most reason people use banks are for loans and we still don't have a good way of providing that service (at least with bitcoins, where people still want to remain anonymous).
What I'm imagining is that traditional big banks would coexist with smaller lending agencies that are using blockchain for processing the loans. More options for getting loans, the better.
Well, there's BTCJam right now. I honestly don't understand how it's still standing up until now because people can just submit IDs of other people. It's so easy to get them on the Internet these days since people are so gullible anyway when doing a deal on the Internet. Even people that are only selling something are uploading their IDs on facebook to prove that they are that person. This opens them to an attack. The picture of their ID and their picture holding the ID are the only two things that you need to submit in BTCJam last time I checked. Those can easily be found in buy and sell groups on facebook (at least in my country that's the case because a lot of people are in that business). You can also simply deceive them by pretending that you're interested in buying something and that you need to see their ID to prove that they are actually the person selling the items. I'm not saying that you should do this but I'm saying that it's one way people get attacked on the Internet. We should be aware of things like this so we can avoid doing it ourselves.
I once asked in slack what about the people that didn't pay in BTCJam. They said that they go to jail. On the other hand, no one should go to jail because of debt according to the law (at least my country's law) so I really have no idea how come BTCJam is still running. The site is probably full of people lending money and never paying them since they can't really go to jail for it. And if anything, will BTCJam do so much effort to put someone in jail when they're on the other side of the world and only owe a couple hundred bucks? Of course not.
What you're saying is probably the most viable way in order to have a legit lending service that will not close down because of people not paying up. Plus if it's small scale, they can probably do collateral.