>> If I showed up to your store with a lump of gold for trade, we would have to go find someone we both trusted to figure out how pure it was. That takes time and money. That inhibits commerce from taking place.

It's the same with paper. If I show up to your store with a note and tell you it's worth x amount, a third party who we both trust has to back up that that note is indeed worth that value.

You're solution, which isn't really a solution at all, is to just have the government take the place of that third party. This is replacing a free market with a coercive monopoly, and carries with it the same repercussions as any other type of anti-free-market regulation.

Now we both still agree to treat my note or gold as having x value because it is endorsed by a third party, but now we choose this third party not out of trust, but because there really isn't much of a choice.

So now that there aren't any competing currencies, innovations like the ones you mentioned will happen much slower, and since maintaining our trust is no longer needed, the criteria for ensuring that a certain paper note or gold piece actually has it's claimed value will be much less strict.

Now the currency-regulator can do things like print too many paper bills, devaluing bills individually, while putting the value of the newly printed bills right into their pocket--and without repercussion.

And I think that's only the tip of the iceberg. Regulating currency is no different than regulating telephone lines or corn.

You said "You can't have a free market if you don't have a viable marketplace to begin with", but government regulated currency isn't a viable marketplace at all, and you really can't build a free market on top of an unfree one anyways.