As Internet and email destroyed work of post offices about letters sending as Bitcoin will destroy banks system about using money. That is my opinion. And I'm pretty Shute that it is going to be as u say - bitcoin or maybe any other of crypto currency will be used mostly by people.
The banks are not used to send money. They provide borrowing and lending service. With bitcoin, they will make more money.
I also agree with you, the banks should have to adopt bitcoin, as with bitcoin everyone is making money even a large number of online companies are also making a good profit from adopting bitcoin, the banks wil also make a good profit from accepting bitcoins for their deposit/withdraw functionalities.