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?
Of course, the introduction of Bitcoin into Banks will cause a change in protocol because Bitcoin and banks works on different principles, thus decentralization and centralization respectively. The Banks may not act as intermediaries during BTC transaction but will own access to the account and balance of the owner/user. The central Bank of India has authorized cryptocurrency and hopefully most of the banks in India will begin to integrate cryptocurrency into their services.