I disagree with a lot of what you said (starting with the importance of janitorial services -- have you ever worked in a place with truly bad janitorial services?) but to stick to the factual side right now, male nurses earn more than female nurses. The article I'll link from the Journal of the American Medical Association includes analysis of approximately 290,000 RNs.
That is my mistake, I would have assumed otherwise. Thus it must make my example invalid. I would have to think otherwise, then.
The point about janitorial services — I am sure having horrible janitors (and horrible customer support) is a true disaster. But being an average janitor is not too hard; if a place has bad janitors, then of course that should be a priority investment.
http://jama.jamanetwork.com/article.aspx?articleid=2208795
It's touching that you think that "gender traits" will give women higher pay in some profession like nursing, but it's only true in porn.