Exactly.
If you are already paying for F, then domestically the only thing you need from any airline is access to their lounges. With AA, that is made simple by getting the AA Executive card which actually gets you a discounted admission to their lounges. i cannot imagine that in someone spending tens of thousands of dollars a year on airlines would be hurt financially by a $450 once a year fee.

Flying international F already gets you lounge access so there is little need to contort your spending and allocation of trips to BA for AA domestic lounge access.

In your situation, the only thing that would concern me is schedule and performance on the route you are currently flying. Everyone has their opinion on each domestic major but for the vast majority of cases, they are surprisingly the same in all aspects.