Yes but FIAT currency has gold as backup.

Bitcoin has FIAT currency as backup.

Something to report to.

Bitcoin would be worthless without the dollar.

So in order for an exchange to actually work, one would have to exchange these bitcoins into stuff that actually have value, like gold or fiat currency.
Either that, or simply just convert all currency to bitcoins, which would be impossible in the next 50-100 years.
In order for bitcoin to have value, people need to offer services and goods in exchange for bitcoins. Then they need to actually be able to do something with those bitcoins in order to get value out of them (i.e. exchange them for money so they can pay their bills/food/etc.).

Do you see my point?
You can have as many exchanges as you'd like. If it's illegal you won't be able to convert the bitcoins to currency. Which means they would be worthless, as FIAT is what gives everything value.

So the bitcoin idea is fundamentally flawed. Unless it can be taxed.