Honestly if you don't want to breed him anymore I would say geld him. Just so the chance of having him breeding isn't there. Or getting loose and breeding to somebody else's horse doesn't happen (I don't know the living conditions, or I you have neighbors ect). I mean if you can control him and understand that he can be unpredictable then by all means its your choice to leave him as a stud as well :)
I just got him with our new mare and I really hope that it works. I'm too old to do another after but I'd never think of cutting him.
Each one is different. Each trainer/owner/rider is different. So each can make their own choices.
I HAVE NOT PROBLEM RIDING WITH OTHERS THAT UNDERSTAND TO GIVE US A LITTLE SPACE. NONE AT ALL.