Health:
Yes, I think there should be responsible supervision of teens (and adults). Especially kids should not be let to disappear for hours with no supervision of what they are drinking. The best is for them to be at your seuda where you can keep track of their drinking and cut them off, or by their rebbe’s house (if he is responsible).
But I don’t see that as being the argument advanced here. I see people arguing that the entire mitzva is inappropriate to the extent it means drunkenness.
In my yeshiva, they used to make sure that every highly intoxicated person had someone watching them, and a garbage can.