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?
Banks have already tried to work on the "problem" of implementation Bitcoin to their system:
https://en.wikipedia.org/wiki/R3_(company)
Financial Times reporter Kadhim Shubber wrote that the new additions are "a sign the industry is gathering behind R3 in one potential implementation of the distributed ledger technology behind the cryptocurrency bitcoin.
Unfortunately, or fortunately, they still fail to find a way how to do that. In short, Bitcoin is the opposite and at the same time the enemy of banks.