Bitcoin is a backing currency. I know this is not commonly known and accepted yet, but it's what it is.
There is nothing that stops people from doing classical banking with Bitcoins. In fact, it is probably necessary, since the block chain is a slow high-maintenance system not really suitable for small transactions.
There's nothing wrong with printing Bitcoin bills. "100 mBTC, to be redeemed at the Malaysian Bitcoin Bank" -- good enough for use in the supermarket. But any larger savings can be stored on your own USB stick, enabling the security and stability of Bitcoin where it's needed. If Malaysia goes haywire, people only lose their shopping cash, and transferring savings out of the country is trivial.
That's the main point why Bitcoin is so great. It works when it matters, but doesn't stop anyone from using cheap, classical methods otherwise. In effect, this will move monetary control away from local governments and institutions, toward international companies and organizations anyone can use from anywhere.
In effect, this means there will be an abundance of choices for banking, and people are not forced to use the local ones. As long as some of them are suitable for non-techies, things will work out. Well, with the exception that uninformed people making stupid decisions are still at risk. But I don't think there's a way to change that.