The problems with Kayle, in a nutshell
1.She's just absolutely terrible for melees to lane against. That's not a problem as long as she's mid lane, but there's no reason she has to stay mid when her matchups are so much better top. Her ranged autoattacks from Righteous Fury allow her to easily poke melee top laners WHILE shoving them under tower and potentially not even drawing minion aggro, and her Q is a very strong counter-engage against most melees.
2.After level 6, there isn't much anybody can do to her because of Intervention's cooldown. It starts at 90 seconds and scales to 60; with CDR it can be as low as 54/45/36 seconds. What this means is that it is almost impossible to fight Kayle with her ult off cooldown. Every single time you fight her after level 6, her ult WILL be up, and she WILL use it to get 2 seconds of invincibility against you. Unless you're extremely far ahead of her (unlikely given her already strong pre-6 game), it's almost impossible to kill her, even with a gank. And if you lose a fight because she ulted, it'll be back up by the time you both get back into lane.
3.She has all the benefits of being ranged without the drawbacks. She can AA poke and safely waveclear like a ranged champion, but also has the sustain and utility of a melee bruiser.
4.Her kit has no counterplay in it. Everything is point and click. If there WAS any counterplay, it would be "never go in range of her empowered autoattacks" and "just never fight her", which isn't counterplay at all. It's just a way to lose lane to her slightly slower.
I'm glad she's not good right now, because if she was she'd be a problem.
edit: god this forum's list formatting is awful