Now, personally I'm with the post above me somewhere that I'm more angry that there's no healer rather than dancer being a healer. But the only reason I had to respond to this thread is because of this post that reeks of condescending ignorance.
Really now? They aren't a thing? Made up completely are they? Did you spend the like... 5 minutes on Google it may have taken you to check your lack of information before you spouted your nonsense?
Melee Healers (Just from my personal experience with MMOs, there are more.)
Friar [Dark Age of Camelot]
Warrior Priest [Warhammer Online]
Disciple of Khaine [Warhammer Online]
Inquisitor [EQ 2 -- with AAs and such, but still]
Chanter [AION]
Here is a forum talking about some of people's favorite Melee healers and the pros/cons of some.
Something of an oddity for something that doesn't exist, wouldn't you say?
Here's another one imagine that.
And to cap off the melee healer section how about I mention The Final Fantasy XI Dancer imagine that... a melee healer and support class in a Final Fantasy game... with the same name of the job that we are discussing shouldn't be a healer.
Ranged Physical Using Healers
Tyrande [Heroes of the Storm]
Ana [Overwatch; Heroes of the Storm] (Who heals with a freaking SNIPER RIFLE I might add)
Spellslinger [Wild Star]
I'm sure there are more out there too, do I really need to go on though? I think I've established that these playstyles for healers do, indeed, exist.