Well, i'm pretty sure it's impossible to fit a 1.60 meter long sword/axe/hammer through a(n invisible) scabbard on your back just by using your arm, they are just to short, and unless you (awkwardly) grab the end of the blade/pole and let it slide slowly, and innacurately into its sheath, and slide out centimeter by centimeter to get it out, you will never swing that thing

So, the point is, wouldn't it be better if the character just held it over his shoulder like real warriors did for greatswords and polearms?

When standing idle, perhaps. When running and especially sprinting the sword should be kept in two hands at about the waist.

I don't really care

I think they look nice on the back. Well, greatswords anyone. Maces and axes look... odd. :S