I think a lot of what people have said already is spot on.
From what I have gathered about banks though.. bitcoin at present is just a pimple compared to them.
They don't care anything about bitcoin and don't expect it to go anywhere.. but they love bitcoin for bringing them blockchain.
You are also true, but the one thing which is becoming problem for the bankers is that bitcoin is anonymous and any transaction of bitcoin do not bring any data about the money that from where that money has came, and it is against the rules of a bank that a person bring some money do not provide source that from where he has earned that money or from whom he got that money.
but again I agree with you as if bitcoin increased to a wide space of the world then they will provide a solution for that matter.