Most supports are mages, some like Lux, Morgana, Orianna, and Zyra can really be either. Morganna is actually my favorite to have on a team, at least if she shield me.
As for Karma's problems - I'd say its mostly around not really having an ultimate, and not having the power in her basic skills to make up for it. Compare her to a support like Janna, and Janna can do most of what Karma can but better. Janna can heal a team with her ultimate, Karma can heal a team with her ultimate (if they're really, really close). Janna can slow down an enemy then run away, Karma can slow down an enemy if she stays relatively close to them. Janna can shield an allied champion and cause them to do bonus damage, Karma can shield an ally and cause additional damage to nearby enemies in the process. Janna can clear waves without putting herself in any danger, with a skill that applies the best type of CC in the game - knock up - as it isn't mitigated by Tenacity and can't be cleansed of Sashed away. Karma can clear waves while putting herself more or less in melee range. Karma "can" increase the movement speed of an ally by considerably more than Janna, but that's pretty much it. Janna increases the movement speed of every allied champion anywhere on the map 24/7 though, which isn't much worse. Beyond that, Janna's ultimate is pretty ultimate. She also has 3 abilities that apply CC - with a slow, a knock-up, and a knock-back.
Karma is pretty fun to play, and 2 enhanced basic abilities really aren't that bad, but being reliable over a 30 second period of time with relatively solid, relatively spammable basic abilities is substantially less useful than being epic for 2 seconds - it's a problem melee carries have as well, were having slighlty better sustained damage/abilities than the next guy is hardly ever more useful than having 1 really epic combo you only need to survive 2 seconds to pull off. Comparing Karma to Janna is a lot like comparing Fiora to Zin Xhao in that regard. And there's really no reason Karma's crowd-control capabilities should be as bad as they are. Her wave and shield abilities aren't to bad, but her speed/slow tether is pretty horrible - even enhanced. For a sudo-ulitmate ability it should at least place her in the highest speed boost capabilities as well - which Jayce, Galio, Zilean, and Orianna hold over her. And of those, only Zilean can't effect an entire team with it/effect himself with it at the same time - but he can use it to hasten or slow, without the tether-limit restrictions, without having to empower it with an ultimate charge, and it's the best speed buff in the game.
But give Karma and actual ultimate, or make 2 of her basic skills feel as game changing as other support ultimates. Even giving her some solid CC for the lanning phase through Tether would be nice - Rocket Grab and Power Fist, Dazzle, Crucendo, there are so many CC abilities on supports that are better than an enhanced slow tether it's pretty sad, really.