Note that these quests aren't just multibox unfriendly, they're grouping unfriendly. Blizz is very inconsistent with this type of thing, there are for example drop quests where the drops are party-wide (though these are rare), and then there are quests like the damn sea monster in dragonblight as previously mentioned. Why the hell she doesn't test/debuff your whole party instead of just the summoner is just plain poor testing.

Sometimes boxing is an advantage with the simulataneous turn in trick, these quests suck all the more if you're trying to play with friends, something this game nominally encourages.