AA actually has a really good amount of paid premium travel. I would venture they skew much higher income/cost than UA/DL. They have lots of business and entertainment contracts for J/F. Why do you think they rolled out a whole sub fleet of EXTREMELY low density 321's on lax/sfo-jfk? They offer "true" F for those willing to pay with flagship checkin and lounges.

The real question is, will these customers start to move to UA/DL due to the much lower prices (it's only a matter of time). If they customers start to move, AA will start dropping prices.