Phosphates feed algae. Perhaps not a cause but having a lot of it isn't a good idea IMHO.
The hair algae is quite tough to rid. The best I do is to twirl it with a toothbrush like what Dennis suggested. Keeps it down for awhile at least for nice patches to grow out of. I have learnt to live with it. sigh. Bleach dip is the last option. here's a
recipe from aquamoss