Kayle players, what is your opinion on her kit?

I have been lucky enough to have played 9 entire games with Kayle so far, and I found her kit very hard to understand. It's not to use her damage abilities, or which builds to go for, since most builds are quite strong. But I honestly can't understand how her ultimate, heal and ultra late game will work out in the early stages of the game. Riot doesn't give out champion abilities just for their show, they do it cause the abilities are meant to match quite well together. But I don't get Kayle abilities at all. Her Q is self-explained, her E is also self-explained, but her W and ult doesn't make sense at all. (To me at least) You make a very selfish champion, who relies getting to her lvl 11 as quickly as possible, which buffs her auto's to the very top. But then riot decided to give her a heal on her W, which has a super long cast animation (Basically 2 auto's of animation cast) and an ultimate, that when used on herself, she can neither use abilities or auto attack. Making it next to completely useless in solo lanes. But, she is neither a good bot lane champion since she is too weak against trades early. Basically have to use the ult on allies to make it work. Yet she has to be this seflish champion, who is meant to gain solo XP to reach lvl 11 as quickly as possible. I don't understand at all. Help me understand what she is meant to do, pre-11.
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