I'd much rather fly Cathay Pacific, Singapore Air or Emirates, myself. Next week I'm flying Singapore, Thai and China Air. I have a short hop of an hour on American, but I can handle that in coach. I'm paying in cash and award miles about $600 roundtrip. I'll get half that value back in frequent flyer miles on the paid legs.
I earn most of my frequent flyer miles in US accounts, but redeem miles on Asian airlines.
There are no US "rules" limiting the number of bags or dictating what the airlines must charge for extra bags, or anything for that matter. Those are business decisions made by each airline. A foreign air carriers flying into the USA can and do permit more charge-free baggage and generally charge less to extra bags.