OK, let's recap:
• There's nothing inevitable about Tank/Healer/DPS or Defender/Leader/Striker/Controller.
• You can't find good examples of those roles in the fantasy literature that inspired D&D (and thus MMOs). You can't find it in comic books or Star Wars, either.
• Tanks emerged because early D&D created a popular class (the magic user) that could not survive under ordinary circumstances.
Which brings us to...
I'll be brief here, because the healer role grows from the same root as the tank role, only more directly: Gary Gygax's simulationist streak.
The simulationist in Gary followed a very reasonable line of thinking: If you get stabbed nearly to death, it should take you days or weeks to recover.
What could be more reasonable than that? It makes perfect sense. But as anyone who has run a long-term campaign knows, long recuperation times can be hell on the ongoing narrative. It's no fun to clear out half a dungeon, then come back after a few weeks to find that the dungeon has realistically been reinforced.
It's worse if some players need to recuperate, but others don't; that's a recipe for splitting the party. And those long recuperation times wreak havoc with any sort of time deadline before the Great Evil Event happens. As a DM, you want that tool in your toolbox.
And it's just as bad on the NPC side. It's not exactly good drama for the PCs to nearly beat the Big Bad Evil Guy, then retreat, then come back a few days later and stab him as BBEG lies there in a hospital bed.
Gygax-the-simulationist wasn't going to allow unrealistic natural recuperation. But if magic is involved, then verisimilitude isn't threatened and all is well, right?
Thus, the cleric: A class that's mandatory not so much for in-battle healing as for its plot-saving fast recuperation. Even a single cure light wounds each day means vastly less time in the village and away from the action.
That's why for 35 years, having a cleric was pretty much mandatory (and even in 4th edition, having a leader makes life a lot easier). Without that healing (or a small fortune in consumables), you ran out of hit points, and then you ran out of fun. You had no other way of getting those hit points back quickly--in combat or between battles.
Gygax's desire for realistic natural healing yields a class (the cleric) that becomes mandatory because it keeps the plot from grinding to a halt for hospital time. MMOs pick up the healer role when they pick up D&D's role differentiation. And bingo! We have another role that seems like it's always been around, but really it's just rooted in a simple but profound design choice made back in the '70s. Had Gygax said, "Screw it--you get your hit points back after a turn (10 minutes) resting," you wouldn't have your leader role today.
Out of Context: It is indeed considered disrespectful to climb me.
Music: Ba Cissoko, Electric Griot Land