The US carriers are relying on their FF programmes to keep their pax flying, despite lousy service relative to the international competition. It's the other US airlines, and their FF programmes, which are the competition.
There's a big problem however: too many FF miles, insufficient redemption and upgrade opportunities, and pax quickly walk. I rather suspect BA's relatively poor treatement of its elites is in part responsible for the success of some of the new business-only carriers, especially Eos.