Her mana costs are undeniably extremely high.
50, 60 and 40 isn't extremely high. It's average, at worst. But it's always important to look at the whole picture - Xayah base mana is on the high end and her mana regen is 16th best in the game. In other words - as long as you don't mindlessly spam abilities for no reason - you will not run out of mana.
Anyways, I mostly wanted to cover this part:
Poor waveclear early.
Because this is simply false. With her Q and passive she has a decent waveclear since level 1, and it gets significantly better the moment she got E - I believe she might have one the best, if not THE best, waveclear from all ADCs early.
Also, her cooldowns outside of her ultimate are on the short side, so no idea where did you get that "Extremely long CD on E" from. 12 seconds for an ability that can snare isn't long - it's normal, if not short (mind you, this is rank 1).
As it is right now - Xayah kit certainly has weaknesses, and it's a working one (unlike some other designs coughKalistacough), but I fear it is overtuned as far as numbers go. You'll see in a week or so, with more Xayah players getting hang of her (and her winrate is increasing fast, especially in higher ranks), that she needs some nerfs. What kind of nerfs - I'm not sure (I have some idea, but there's no need for me to post them, Rito will figure something out). I just hope they will just straight up nerf her damage output rather than unique strengths.