This idea is already too far-fetched. Look at Bitcoin right now, some are saying it can be controlled by China and if there is even a slight truth on that then I don't think any nation will ever allow their banks (including central banks) be gobbled by Bitcoin. Look at the current debate on hard fork right now...it is a divisive debate and one that exposed so many vested interest...with that story on the backdrop do we really think Bitcoin and the community behind it be given a chance to wipe out banks and be the banking industry itself. No, what am sure is that the banking industry would soon adopt some idea of the blockchain or any from the cryptocurrency industry. Bitcoin and the banks can be complimenting each other not that they will kill each other. The internet did not kill radio, tv and even the printed newspaper are still around and can also be adopting the situation all in the name of survival. We are entering a very diversified and very "niched" society so we have a place for any industry and for anyone.
"I did not kill my ancestors, therefore, other new innovations wouldn't either."
It doesn't matter if that's the case for the Internet. Bitcoin is different. You can't just look at other things and be "Ohh, Bitcoin will do that as well. They will have the same logic." I'm not dismissing the possibility of that happening, but I'm saying is that you're basing what will happen to X stuff from what has happened to Y stuff.
The internet did not kill radio, tv, and the newspaper. Yet, all of that is just a small part of the Internet. Today, you can do that using the internet. Radios are aired online as well. For tv, we have netflix. And for newspaper, we have Google, Yahoo, and almost all news articles are already posted on the Internet.
Since you like applying the same logic of Y to X. How about this? It will be the same. Fiat will just be a small part of bitcoin as well. And all of the things that you can do with fiat, is just a small part of bitcoin. Actually that's the case already. But bitcoin user base is still nothing compared to fiat's user base.