I didn't want to go into spoilers too heavily there, but yes, I completely agree with your read of Kara's motivations in the comic. Kara sees herself and the tumultuous past she'd been struggling with in the younger girl and that really only works if Kara's notably older than her.
And yes, I love Clark as much as most anyone else here does, but he really has no place in this particular story. It's Kara's story and it really does help establish how great and different of a character she is compared to her cousin.
BTW, I'll just go ahead and say this; For anyone here who hasn't actually read Supergirl: Woman of Tomorrow yet, I strongly urge you to go ahead and check it out as soon as you can. It's a phenomenal comic and some of the best work I've personally seen from Tom King. That said, if you are someone who prefers for Kara to be significantly younger than Clark in the present day, I do think you will likely have to accept that loss ahead of time as the emotional crux and point of the story of WoT essentially requires Kara to be a few years older than fans are used to. But trust me, it absolutely makes sense in context.