Karma's Identity
I've been seeing a lot of threads recently complaining about Karma, about how she has no identity and no reason to pick her over other utility-mages, and that she feels boring because of a too-heavy emphasis on Soulflare (RQ). This thread is about my take on these issues, as a heavy Karma player.

What is Karma's identity? Karma is a poke-focused utility-mage with an emphasis on anti-initiation. She is good at poking an entire enemy team with constant AoE harass, while keeping herself fairly safe with her shield and move speed. She also excels at keeping juggernaut-like champions (such as Nasus, Udyr, Darius) away from her team with her combination of ranged AoE slow, targetted root, and AoE shield/speed boost. The shield also lets her roam and reposition easily, and allows her to move into good positions to poke and to trade favourably.
Why would I pick Karma over ____?
Karma falls into the utility-mage class, alongside the likes of:
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While she can (and often is) played in the support role, her focus is still more on being a utility mage than an outright support.
You would pick Karma is you want a safe mid-laner with strong AoE poking ability, combined with the ability to peel and protect another high-priority target (e.g. a strong ADC) if necessary.
For example: you have a poke composition, the enemy have Nasus, and you want to both poke them down while keeping your Kog'maw safe.
The other champion who comes closest to what her kit provides would be Lulu. Both have AoE poke, speed boost, and protection spells for themselves/their teammates. The main difference is that Lulu has a heavier focus on protection, while Karma is more focused on low-cooldown (and longer-ranged) team poke.
The other utility mages are generally more oriented towards making picks (Lux, Morg), area control (Ori, Zyra), or disengage (Morg, Zyra, Ori.)
Thematic identity The old Karma had a very strong thematic identity of duality. Her spells could each be used in aggressive or defensive ways, with her mantra adding bonus effects to shift from the one to the other. While her old kit had some flaws, it certainly made her thematically unique and interesting. The new Karma theme is shifted instead towards having to choose which of her three abilities to empower, making that one do "the same, only better" rather than adding a thematically opposite effect - something which may work better from a gameplay perspective, but is much weaker from a thematic perspective.
Why Karma's mantra system feels bad The problem with Karma's Mantra system is that in most cases, one option (RQ) feels the most impactful and powerful to use. It becomes less of a choice of which of her empowered abilities to use, but rather a case of using one 90% of the time, and only occasionally using the others. Simply put, dealing a huge chunk of damage to the enemy team usually feels more useful than locking one of them down for a little longer or shielding your entire own team. Sure, sometimes you want to make those clutch heal saves with RW, and occasionally you want to speed your team somewhere or protect from some incoming AoE, but most of the time you'll be wanting to RQ the enemy.
RQ is also the ability which can (when used properly) give the most benefit from her passive. Hitting the entire team can reduce her Mantra's cooldown to around 5 seconds, which is huge. In comparison, her RW can reduce it to around 11 seconds, and her RE doesn't interact with her passive at all, effectively making it have a much longer cooldown than either of the other empowered abilities.
Shield-bombing One of Karma's old iconic spells was her shield-bomb, dealing instant AoE damage around her shield target when using Mantra. This followed her theme of duality, and also gave her a way to proc her passive when using her shield. However, I can understand why Riot removed it. An instant AoE nuke has very little counterplay, especially against mêlée champions who have no choice but to go near Karma's allied champions (to try to kill them) or minions (to try to farm them.) Note that there are almost no instant AoE abilities in the game (outside of Lissandra, and some low-sustaint-damage cases such as Karthus, Anivia, Swain.) [Edit: Not saying I agree with this, just that I can see the reasoning.] However, as mentioned, this means that her RE now has no interaction with her passive, making it her most-expensive and least-impactful-feeling spell. Letting her proc her passive on every target shielded after the first would help alleviate this problem (though perhaps being able to easily and reliably reduce her Mantra's cooldown to 8 seconds would be too much.)
Summary In summary, Karma has some unique traits and reasons to pick her, but falls short thematically, and her gameplay hook of having to make choices as to which spell to empower falls somewhat flat because RW and RE are just much less appealing than RQ in nearly all situations - especially when you consider that RE is her only empowered ability that doesn't interact with her passive.
Who am I? I guess I should add that Karma is one of my main champions (second-highest mastery), and that I played her both before and after her rework - much more after the rework, though. I originally picked her up because I preferred the less-played champions, and mostly played her as support because it was very awkward to find a place for her in a team (plus, people tended to flame.) Since the rework, I've played a lot more, but exclusively as a mid-laner. I've played Karma a lot in high gold-low platinum over the last few seasons.