Well I can't comment from a healer standpoint, but from a DPS standpoint, I do get worried, when I have more health than the tank does (I have 24k unbuffed as dps).
Especially in some of the harder instances, like ToC or the ICC instances.
I will switch to tank gear/spec and dps. Which has saved the group from wipes a few times, after the tank died. Like during the Black Knight on phase 3.