Banks will have to adapt to this new landscape or they face being replaced.
I see the bank's function as being a trusted and regulated gateway on top of the Tangle. For example, my grandma is never going to download a crypto wallet, but hopefully in the near future her bank will let her take advantage of this new tech.
Of course, the option will also exist for all of us to be in control of our money without the banks, the original intent of crypto.
Yeah some banks are already begining to accept them. Some top Major banks use ripple for international transactions.
Litecoin as well recently partnered with a deutsch bank owning about 10% of its share and as well collaborative effort to be used for their foreign transactions and loyalty programme.
Soon banks and financial institution would stop fighting it and accept it generally.
Crypto wont necessarily replace banks both can co run together..