Accepting Bitcoin in banks will take a lot of time but it will come gradually , when they're filled with pressure from the populace they will have no choice.
In essence, we are going to have a time when banks would have a public address and have Bitcoin investors deposit into them, just the way we have with exchangers… well, that’s possible but doesn’t sound very logical at this time to me.
The ownership of our Bitcoins is manly having to own a private key or seed phrase to the wallet its stored in and this wouldn’t be the initiatives banks would want to use in any eventuality, they would want control and you know it’s a wrong idea giving a 3rd party a great deal of control over your Bitcoin.