....Couldn't the Fed artificially fix "an exchange rate between" USD and BTC such that USD would be "the over-valued money" and BTC "the artificially under-valued money"?
Sure. Many governments have tried such things, and a black market develops to compensate for the differences in values. Those are already in place all over the world. But yes, the stupid things that governments did yesterday are to be repeated tomorrow.
The problem is this. Suppose that a government placed restrictions on Bitcoin. Then in that country, someone....a police officer, a judge, a politician....wants to buy a $6 replacement battery for his cell phone. He looks on Ebay (etc) and finds the cheapest, easiest way to buy it is from Hong Kong with Bitcoin. A couple clicks later it's done.
Aggregate those individual purchasing decisions by millions or billions and you have the behavior of nations. Some laws are simply disregarded.