if the tank melts in 2-3 seconds from 3 mobs, OP's own words, so fast that he couldn't press his own cooldowns, a healer would not be able to save him either, yet he expected them to do so
which is why I don't buy the OP's story that the second group had no problems, tbh
you're generalizing every healer over a group of people wanting to heal more things, yet forgot to mention that just about as much want more dps spells, probably about the same amount of players want both and a fourth group is happy as is