As I understand it, iron is required less for men as it is women; for just what you said regarding women bleeding. See info on this web site. caffeine will cause iron not to be absorbed. I don't drink any caffeine; probably unlike most men. So build up of iron is not good for "me". Too much build up will constipate both sexes.
"Constipation is a common side effect of taking iron supplements. To help relieve constipation, slowly increase the fiber in your diet by including whole grain breads, cereals, fruits, and vegetables. Drinking at least 8 cups of fluids daily and increasing moderate exercise (as recommended by your physician) can also help you avoid constipation."
...and I don't believe in this "more water" junk. I'm overloaded with water daily for over a year.