And to do this, that means that you need some trusted way to determine the price of Bitcoin 1.0 versus Bitcoin 2.0.
Which means you need a centralized place, let's call it an exchange, to determine the rates between the two version. Since you probably want the rates to be consistent across the entire network at any given time(otherwise, what's the point of a non-inflationary currency), it's probably a decent idea to maintain a centralized location for that that decides the rates. A decentralized method may be possible, but I sincerely doubt that it will work in a way that would actually encourage people to convert to the other currency to purchase things.
In either case, you still need something that can regulate the transactions to make sure that everyone is behaving correctly. If people aren't(which should be the first assumption you make about anything), you'll need some method of dealing with it.
So... yeah. You just created the Federal Reserve and money markets.
Realistically, given that it's a democratically run, the current Bitcoin implementation is in the same boat, if the biggest users decide to change their policies, the entire network can end up in a similar situation where a Bitcoin from X is worth a different amount from a Bitcoin from Y.
I don't really understand how Bitcoin is better than the current currency system. It's just different because it's on the internet.