Dani Rodrik asks:
Whether you like it or not, the WTO is the only international organization in existence that actually makes the U.S. do what it would not otherwise have done on its own. No other organization has such power. I would love it if somebody would come up with a sensible story as to why the U.S. has ceded so much power in trade, while zealously guarding its sovereignty and right to unilateral action in every other domain.
One part of the answer may be: Because the U.S. wants a trade regime that can pry open foreign countries' markets, so it is willing to give up sovereignty to get that. In other policy areas, it wants to coerce foreign behavior to a much lesser extent.
Another part may be that there are people in the U.S. who want to open the U.S. market (and thus cede sovereignty) and this is a way to achieve that (unilateral market opening won't be politically feasible).
Perhaps the answer lies in the combined effect of these two things -- a strong desire for foreign market access and a weak desire to give access to our own markets.