Nobody has to accept paper money, either. The only thing "legal tender" laws mean is that if you want to use the power of government to enforce debts, then the government gets to say that its job is done when government-declared legal tender has been presented, whether you accept it or not.
If you don't choose to involve the government in your affairs, then legal tender laws don't affect you.
A copper coin worth $20 in todays USD would weight nearly 3 kilograms!
Surely at least paper gold and silver certificates would be a reasonable concession.
It's sort of a bogus loan, with a variable term and zero interest rate, but it's still allowed, and certainly makes things more convenient for a lot of people. And the government can still profit from the seignorage from the mint.
I think it is less important that our money be a particular commodity than it is that the government lack the power to manipulate its value for its own convenience.
In my opinion, it is clear that the power to "coin money and regulate the value thereof" is to standardize the exchange rates between coins, probably by weight of the metal, but not necessarily. It is also clear that the coins need not be metal, but also that no one could be forced to accept coins other than gold or silver coins.
Thus, they could stamp out wooden nickels, but that wouldn't make them worth anything to anybody, except possibly for payment of federal taxes. As long as we have those, it is only a short hop to rectangular paper "coins". They can do it, but nobody has to accept them.
But since nobody is trying to pay taxes with Bitcoin yet, and the federal government isn't mining them, as far as we know, there is no justification for them to be standardized or otherwise regulated whatsoever. It might arguably be authorized under whatever clause, but it certainly isn't justified.