I'm not sure it makes sense. LAX/SFO-JFK are lucrative and extremely competitive when it comes to the highest yielding traffic. AA sees value in investing in what it sees as the competitive advantage of a premium-heavy aircraft with 3 cabins on those routes, and related investments in Flagship Lounges, Flagship First dining, etc.

If you look at markets like PHL (which might not exactly lose money with a configuration like you describe) and CLT (which might), there is no reason for them to offer anything more, because they own that market share and don't have to compete for it.