I have to admit that I'm sceptical about Bitcoin. I'll give you my reasons, then please convince me!
Bitcoin is not backed by anything. It would probably not exist in a free market.
Fiat isn't backed by anything either. Bitcoin is an revolutionary economic experiument in my opinion.
Money in a free market has always been some kind of commodity. Something that has value beyond its use as a currency. The problem with Bitcoin is that it has no value beyond its use as a currency. Why should it then be regarded as money? Money came into being as a medium of exchange, so that if you got stuck with it it was useful in some way. It wasn't just a piece of paper. It was something that was useful in and of itself. Like gold. Like silver. Bitcoin has none of that. It's just a string of 0s and 1s. Where does it get its value from? I don't think in a free market it would be valued.
Something like Bitcoin could be used as a currency if it was backed by some commodity to do anonymous/quick transactions, but there would be a standard, ultimately, for exchange. It would always be exchangeable into e.g. gold. So that the banks who issued the Bitcoins were contractually obligated to redeem them into gold. Then Bitcoin would serve as a currency, but the money would be the gold.
It's already being used as a currency so you're wrong, though it's not ideal currently with price fluctuations but this could change in the future.