If a geared healer can't keep a geared tank alive in big pulls (barring rare exceptions like the 3rd Shisui pull) then frankly I think they're being selfish by refusing to learn their role/play properly.
Outside of savage/EX content, I don't expect healers to DPS (I wholeheartedly encourage it but understand how people might not feel comfortable doing so - and that's fine because it's casual content). I expect them to keep me alive first and foremost, and they have more than enough tools to do so.