I can picture a wizard/monk striking someone with Vampiric Touch strike 5 times on their turn and adding their unarmed damage plus ability mod. Ya know, cuz that'd be cool.
Or an eldritch knight doing it 9 times with the right feats. Cuz why not?
Well, generally you get 1 reaction per turn, meaning 1 attack of opportunity. Also I would suggest the magic only allows a single touch per turn, meaning if a player has used it on their go they cannot use it as an AoO. You are right that balance is important, even if you are unable to actually depict with a modicum of respect for people attempting to create a balanced ruling on the subject.