No Karma in pseudocarry supports? Morgana being higher than Karma in buffer supports? Missing her in initiator support group? Dude, please - this support is simply MADE to poke enemy, punish them for ANY misposition and brings strong damage and utility to team. Karma makes wonders in yoloQ - you can shield ally (or whole team) to keep him alive and/or get him into/out of the fray, you can leash enemy to pick up easy kill for your team, you can deal superb damage (don't underestimate this - her damage potential is higher than most of supports, even early on). You even have some potential to initiate fights with her - any mispositioned enemy who get's hit by RQ or stopped by W might be in grave position, and you can even cast RE to speed up allies (and also shield/damage). She isn't easy to play and she is weaker against enemies who know how to position themselves, but she isn't that weak.
I just feel that you missed strongest poke support in the League and made her tier 3. Another strong damaging support (who brings even more utility) - Lulu, also tier 3. And why the hell Thresh is god tier? I don't find him god of yoloQ with WINRATE BELOW KARMA'S. Even more, Karma could rise for above 50% in diamond soloQ, Thresh couldn't. (It's hard to compare them to support Lulu, as some people still play her mostly on the other lanes.) I don't doubt that Janna is one of the strongest, but Sona... Again, strong, but not godlike. I'd say it's more frustrating to play against Nami.
BTW. Try zoning enemy with Cait-Karma lane. Most of enemies are helpless against them, it's really fun to see them constantly denying farm (or heavily punishing enemy for trying).
Outrange Karma... wait, what? Who can outrange her RQ poke? That's one of biggest threats on botlane.
About engages on her early on... there are very few champions who can do this (most likely, Leona who manages to catch you with E). Most of them are quite ineffective, because Karma can kite them with shield if needed. And I hope you picked AD with godlike earlygame kill potential (such as Lucian), because if you didn't - Karma and her ADC will most likely punish you for any kind of engage. Her damage is no joke, I've won countless 2v2 on botlane and lost a few of them.
Yes, outsustaining her is an option. This is actually strongest counter to poke lane - enemy who can recover from poke and farm their way back into the game. However, I'd say the one with biggest threats to Karma as it goes to sustain is... Nami. Not Soraka (considering you will dodge her Qs, which is not really hard thing to do), not Sona (who is just terribly squishy).
Of course Karma lane is likely to push it - she pokes hard after all and makes you go back to your tower. This is high risk, cause you might get ganked, but also high reward - enemy is scared and kept low HP most of the times.
It's not that I find Karma godtier - she is quite far from that. I just don't get how could Thresh be considered godlike, while Karma is tier 3. He belongs tops to the T1, while Karma should be at least tier 2, along with few other changes.