Yes, while that would be personally satisfying and ultimately an excellent form of discipline... (Tells the little buggers you can't act this way in public either.)...do you realize how many goody two shoes are out there who would turn you in to kiddy protection rackets if you so much as glare at the brat?
There used to a thing known as social discipline (practiced in many other species unlike ours now) where a totally unrelated person could whack the shit out of a miscreant. Said miscreant would go home and whine about it, and proceed to get another whacking.
No more.
As much as we dislike misbehaving little pieces of garbage, there are those out there who will prevent a well meaning parent who is trying to raise a decent human being out of a snotty little prick.
Sadly, most people are not willing to do what is necessary when bratleigh and snotgrass act up in public. Namely, they get removed from the premises, taken home and disciplined, plus also being denied any little 'perks' for the next month. (which is the only thing that seems to get the little darlings attention.)
Of course, the easiest is merely to get a baby sitter. (money money money....)