Just to nit-pick, this is not the reason why AA status members don't get domestic lounge access. It's because AA has a profitable (?) club membership scheme.
If I were AA, I would try to make the airline more profitable rather than have a profitable club membership.
AA EXPs have plenty of bonus miles while CX DMs don't. My view is that AA gives her members a choice of using 50-85K of their 120K+ bonus miles on AC memberships.