So I bought her since she was released, and it's pretty obvious, there's NO way she can keep up with Sona or Janna. In addition, she's so poorly designed that her unique nature doesn't really matter. Here's the rundown why she's a terrible hero.
-1) Terrible passive.
The ability to gain more AP the less health you have COULD be a nice idea, just not on her.
First of all, Karma should NEVER hang around with low health, one focus and she's done for. Since people make it a point to target the support first, so even if you DO get lucky and manage to escape with low health, it's suicide to stick around with your "uber ap". Since her heal is short ranged, she has to get back into the fight to contribute some heals. Not to mention, it gives the enemy team even more reason to focus you down. Overall, terrible idea for a support to have.
Also, hilariously, try playing karma versus Veigar's ult. "Oh so you get more ap the less health you have.... PRIMORDIAL BURST..... dead from half health...
-2) Her "Heal" is terrible.
First you need to use a Mantra charge just to use it. That in itself makes it inferior to other champion's heals. Then it's the fact that it's "attached" to her Heavenly Wave. Now, on paper, having a spell that both damages enemies AND heals allies would be overpowered, but it'll mostly result in unwanted pushing of lanes, accidental minion aggro, and killsteals. In high ELO stealing kills from your carry because you were only trying to heal will piss people off.
Lastly, extra AP does NOT increase the fixed heal amount, only the percentage one. Ignoring the fact that you need 250 AP JUST for another 5% bonus heal. (so you heal for 10% of an opponent's missing health, soo on a guy who's missing 1000 hp you heal for 100, wow...).
-3) Her Spirit Bond is unwieldy, and criminally weak at lower ranks.
This spell was terribly designed... End of story. In order to actually get to use it's AOE slow and damage it requires that you pass the beam through the target. So, either you need to make the guy you just leashed run around the field (negating the movement speed buff to begin with), or that you step OUT of position, in order to try to maneuver around your enemies, exposing yourself to a gank. Although the 300 damage does sound nice in theory, it requires too much busy work to get the most out of it. Also, the mantra effect is pathetic, since you're at most getting a 40% slow, which even orianna has on her spells.....
-4) Her rank 6 spells are pathetic.
One of her supposed strong points is , that since she's lacking a proper ult, her normals abilities have 6 ranks instead of 5. But instead of being stronger than other characters' skills, it simply means that their effects are spread out more, requiring MORE levels to get to the point where you'd be as strong as comparable characters.
People keep telling me that Karma isn't a true support, but rather a mage with support characteristics. If that really is true, there really ISN'T any reason to play her.
So, let's look at "mage" karma.
Her full combo is Heavenly Wave, Followed by a mantra shield, then Spiritbonding SOMETHING other than her target so that the beam passes through them.
Well, you need a mantra charge to use the shield's damage, and since the shield has a 600 AOE, you won't always be able to target yourself with the shield, and you won't always be able to use it. And you need to cast your Spirit Bond in such a way that the beam passes through the target. IF there aren't any creeps nearby, good luck....
But worse than that it's her items. Karma requires AP to keep up with other enemy mages, so she needs to farm , thusly minimizing her role as a support EVEN MORE.
Yes, her shields and heals will be better, but early on it;ll mean less money spent on wards, less money for your carries, and any accidental killsteals from the damage her heal and shield do. So, why not just get a mage?
Lastly, think about it this way: Do all the additional effects her mantra charges get REALLY offset the bonuses from something like Sona's AOE supress, Soraka's Global heal, or Janna's knockback?
Conclusion. She's weak and poorly designed. You want a hybrid healer? Play Taric or Nidalee instead.