Banks are already working in hand with crypto companies as we speak right now.
For example, in my country ripple is working with two banks to help them get their transactions faster and cheaper.
Yes, I don't like ripple but that means banks that are working with ripple are looking into crypto and if they succeed and get better deals thanks to ripple they may also start to hire more blockchain developers themselves and move into in-house system which would be awesome.
Banks will not become blockchain based over night, that could never happen, these are trillion dollar goliaths that are super high end, it will take years before they could even slightly alter anything, even digital banking took over 10 years to reach where it is right now and we still have a long way to go, but as long as it is in the path right now that means we will get there eventually.
You are right, some banks already work with some crypto currencies, ripple is just one of them. Some banks will do it like that, they will just take existing coins and they will develop their business with them, but some banks will make their own coin or token, they will create their chain, explorer.
Generally it's what we discussed here on forum years ago, that one day entire banking system will use blockchain in one way or another. Blockchain is better, its faster and more secured, traditional systems don't have a chance against blockchain. We are in the middle of transition times, I believe that first banks that fully embrace blockchain will be the banks that will be on top.