If any banks had a clue (and a desire not to become extinct), they'd already be lining up to win your business in being the holder of your coins/millibits.

I'm not saying I'd be a customer necessarily, but on the whole people don't want responsibility for their own decisions and would see it as a sensible move.  [opportunity with neon lights and bells on it!  hello? anybody here? nope, no banks, they want to keep the model as it is].

The banks could make a sh1t ton as they transitioned out of the old to the new, maybe give you 10% pa, rather than 0% on fiat.  Grandma would like that.