Or you simply adjust your pulling, 95% of pulls can be solved by something like.

Sprint > go close > mob spots you and queues its first attack (even if a regen was to tick now the mob would run to you) > tank aoe > get next set.

If you however pull with ranged the mobs will run towards you ... your Global wont be up again by the time they reach you, they hit you once and go for the healer.

So yea regen on pull is no problem if the tank adjusts, if they want to do that is up to them ... but its not "omg i cant tank cuz i get regen during pull"

Cant kill them all the healer likely thinks hes doing his bestm

Sch has this problem by default now. If your fairy heals the tank (she will cast this on 99% hp) she would get hate ... however the fairy cant be targeted anymore so it goes straight for the sch.