It will never replace Fiat, most people don't want to be resposible for the security of their money. That's why banks exist, for ease and simplicity. Blockchain payments may facilitate inter-bank and inter-processor transactions on the back-end where slow transactions are not a problem, but will never be widely accepted for mass person to person payments.

Bitcoin will never be that back-end blockchain, a large scale financial system would most likely require coins that are created by the banks, transacted on the network and destroyed by the banks when the funds are withdrawn. It would be an alterntave to crediting a bank account, you provide a pubkey and the bank creates a start transaction signed by them containing the amount requested. When it's time to withdraw, you send it back to a bank and the network then marks that chain of transactions as expired and can't be used anymore.

Of course, the old inter-bank payment system still needs to exist behind this, so really it's pointless until the entire banking system moves away from old, slow, monolithic back-end accounting systems.