I've tried 4E a couple times now (some gents graciously allowing me to join their game) but I haven't gotten to experience "real" Minions. In this game's house rules, Minions have reduced HP but not 1.
I'd prefer if they had only 1 HP. My biggest complaint about 4E's gameplay, philosophical issues aside, is that everything has a preposterous amount of hit points. Even scabby caravan guards can have like 60 HP. Remember when Conan had to stand around hitting toothless, minimum-wage palookas like 20 times each with his claymore before these tireless yahoos would drop? Neither do I... I also do not remember that.
My approach in OD&D and other old school games is just to say that the vast majority of guards, soldiers, thugs, etc. are either "Normal Men" or 1st level Fighting Men... thus usually having 3-5 HP (a big dude might have 1 or 2 more, a scrawny dude 1 less). Which means that a PC Fighting Man is going to get 1 attack per round per level against most of them, and if he is strong like Conan (15+) and has a two-hander he rolls 1d6+2 damage... which will usually mean a one shot kill on these clowns. Which is as it should be, going from the source literature.
So... I don't think I would have a problem with 1 HP minions. In fact, I'd prefer if that was the norm. Because otherwise, in 4E, Joe Bandit is about as tough as the Hulk.