I play PTW, Regent/Monarch and America is my favorite civ. Ision hit the nail on the head- it rewards a more sophisticated playing style and can be very powerful in the right hands. In PTW Industrious is probably (is there consensus?) the most powerful trait, and I think Expansionist is the most underrated. I personally prefer it over Militaristic for sure, and probably Scientific and Religious as well. It's only really useful in the first half of the AA, but that is the most critical phase of the game. You won't wipe out a neighbor with an archer rush, but if you can make contact with two groups of civs that are isolated from each other, the tech brokering opportunities can put the game on ice while you are still in Despotism.
There are plenty of other civs with an inconvenient UU -- either early ones that trigger a despotic GA, or defensive units that don't always let you start a GA on your own terms. I've never been very good at incorporating a GA into my game strategy; I tend to treat them and Leaders as a pleasant bonus that I can live without.