Sticking to one is really dumb
You get nothing extra on AA for over 100K miles - it would be really stupid (and I also would not want to offend anyone - touche) to stick to just that one, when being BA gold gets me admission not only to all of the BA clubrooms, but saves me $300/yr on Admirals Club because I can access any Admirals Club, or even the Flagship Lounge, when I am travelling on AA. Thus I can do something in Chicago no AA domestic traveller can - use the quiet, uncrowded Flagship Lounge, and enjoy sushi and hot hors dourves whn I connect in ORD.