Not sure how much the showers cost to operate. If I want to use water, I can go in the restroom and turn on the facet. You need a clean towel - not sure what that costs. At IAH - CO and then UA had washer/dryers and the attendant washed the towels. Is the labor cost much different than the person going around and collecting glasses in the club?
Years back when CO hooked up with QF after CO discontinued service to Australia, I would book many reward tickets in QF premium cabin with continuing flight on CO in F.
CO did not have showers at LAX, which was a problem. At least when CO was in Skyteam you could go over and use the showers in the Delta club, via the connector. CO started improving its lounges at its hubs (just that LAX wasn't a hub).
The big plus for AA is that EXP gets access to Flagship lounges, with big buffet food and showers. UA should let 1Ks in the Polaris Lounges (like they do GS). AA allows both EXP and CK.