That was the intent, just as Congress has mislabeled several other laws as "civil rights" or "tax reform" which are not really what they purport to be.
We can have free trade any time we want it without negotiating treaties or "agreements" that skirt the Constitution's ratification process. Just drop restrictive tariffs and trade embargoes. My son could go for a good Cuban cigar (I don't smoke, but I do care).
As far as "internationalist-libertarian" wet dreams go, perhaps you've forgotten that both the Cato Institute and the Libertarian Party were fully in support of NAFTA.
We either have a government that believes its citizens should be empowered to buy and sell freely or we don't.
The nature of bipartisan "agreements" on trade over the last decade indicate strongly that we don't.
I agree that we don't have true Free Trade. Aside from Cuban cigars, which are a corner case, the NAFTA treaty was 2000 pages long with all sorts of rules for everything. I tried to bring a few cases of Tecate back from a short trip to Ensenada, Mexico and was told the "limit" was six cans per adult.
Imagine that. Post Free-trade agreemnet and GM can move an entire factory to Mexico but a US citizen can't bring back a case of beer.
The full on Free Trade fundamentalists often also support unlimited immigration and other extremely idealistic positions. Because we have little experience, and none in modern times, of what these super-libertarian systems would be like in practice it's hard to judge what the results would be.
Like it or not governments are a big part of the world. I guess I don't think our can unilaterally surrender while others view economics as war.