If Bitcoins were introduced in banks, there'd be probably a different protocol made by banks if I'm correct? What would it be like?
It would definitely use Blockchain instead of the regular web applications to do bank operations.
Of course that wouldn't come overnight, it will be a big switch and slow change but it will definitely happen due to all the advantages of Blockchain over the regular interconnection of today. And when Bitcoin is one of the main waves if not the main one then everybody will take Bitcoin seriously.