yes it could, maybe the system will be different from the Bank, because the Bitcoin system is run by Blockchain, and maybe the Bank can cooperate with Bitcoin, by implementing Blockchain technology on the banking transaction system.
I believe it's already replacing the system. Banks are heavily investing in using blockchain technology for their internal needs. They won't get bankrupt because of bitcoin, they're trying to find the ways to apply blockchain, so when bitcoin takes over fiat in some parts of the world, they will still be able to offer derivates and other markets.