I think in the future banks will be able to store your crypto and also exchange it. I'm happy to see that crypto is finally waking up after the winter 
You say about crypto and bank link. It will happen or not we are not sure. But I do not think bank need linking with crypto.
Although banking system always good. But as my personal decision is Crypto will be rise without any help (include bank). Crypto trx system is blockchain based, which is the most perfect system and all over great. So, Crypto makes life easier without banking.
I agree with you that crypto does not need a bank.
because I personally think both have the same benefits as saving money, but have different functions and different systems.