Playing him requires more finesse than people think. The finesse is contrasted by his manly, large model and brutish feeling.
If you see a
when he's skillfully kiting people with W's and Q's to apply bleed, sustain, all while keeping them in reach without getting to close before he finally goes in for the dunk is amazing.
Also, when you see him consistently leap through the air beheading champ after champ it's a rush like no other.
Another thing I like is upon reaching five stacks, the entire screen reddens and you can almost FEEL the power you just received.
Watching people smirk as you're about to die before you land a three man decimate healing for over 40% of your missing HP (with spirit visage and runic armor). You laugh back as you recognize that in your hands is League's only champion who can tank like a poppy, sustain like a vladimir, and finish off people with almost assassin-level damage.
The trade off? I run like I had 20 big macs. But hey, the massive armor is heavy ya know? 
UNMATCHED POWER 
I respect the katarina reasons in the OP. Especially the cuteness, she's easily the hottest League character for me (lata ahri ya dumb bish) and second only to Rek Sai (Kappa).