I'd rather say Bitcoin is the Future (Why Only Future?!) Alternative to Banking.
It might never replace fiat for two reasons, IMO:
1. Anonymity
Can you imagine a top-secret spy being openly a top FB star, vlogger, or blogger? Doesn't it sound ironic/absurd to you? It does to me.
However, I do hope the developers might come up with a new technology allowing for client identification (kind of KYC) without disclosing the client's identity. Sounds paradoxical, but it doesn't mean it cannot be achieved. Whoever could have thought we would have something like Bitcoin today?
2. Banking interest
With Bitcoin used in banking transactions, banks' role seems to be like an intermediary's one. Do you believe banks would be willing to do so free of charge? I don't think so. If they get involved, we'll have to pay some kind of fees or commissions to the banks, i.e. the transaction costs are going to go up. Why would we want to pay more when we can do the same without banks as intermediaries with their extra fees? I don't understand.