I've had a feeling of disappointment with new champions for a while. Let's talk about that.
This is not directed solely to the release of Kayn, for me personally it's a much longer sort of unhappiness. Some background: I started playing in season four (and am currently Plat 2), but didn't really pay attention to teasers and release information -- the earliest champion release I can remember that I read up on was Bard.
Here is a list of the releases since then from oldest to newest:

Some of these champions are amazing, with really thought through identities and I consider them good additions to the game. But personally, none of them click with me. I do have a PBE account, so I was able to play these new releases even when they're hype was at apex. I just don't enjoy playing as them, with a few small exceptions. Why? I'm not sure -- that's where the discussion comes in to play.
Here a few small issues that I have that are more champion specific, just for some context from myself.
- I feel like Kindred's theme was a huge miss on the rift. Wolf has next to no in game relevance, and the abilities have little meaning to the champion with the exception of trying to make up for wolf's exclusion to the character as "they". I was looking forward to a champion with two controllable entities, even if it meant shipping an experimental concept to test.
- Aurelion Sol seems like he needs more focus on his stars. The revolving concept was a good choice, but making the only related ability simply make the stars extend seemed like the potential was thrown away.
- Rakan doesn't feel unique. I'm sorry for those of you who main him or really like him, but he feels like a complimentary character to Xayah. The only exception to this in my opinion is his ult, which was a step in a better direction. Other than that, he just seems like the support for Xayah, which yes that is part of his theme, but it ruins his individuality as a released champion.
But there's something more exact that makes these champions unappealing to me.
I used to main Shaco (pre-rework), and currently main Kha'Zix. Yes, I'll probably get some hate for that but I have my reasons for liking them. They feel responsive. They have small parts that make the difference between an alright and excellent player. Shaco has his small window of invulnerability in his ult, his box placement mechanics that give instant cc feedback, and an overall feel like the mind games of the character are meaningful and direct (still referring to pre-rework Shaco). Kha'Zix is an even better example of what I mean. His Q has fluidity with his E (able to be cast during it), his W can be buffered and flashed with (like an Alistar flash pulverize), you can flash in the middle of his leap, and his ult is instant stealth to the keypress (even if it doesn't last long).
I don't like clunkiness. I don't like over exaggerated animations. This is why I think I'm unhappy with new champions. I'm attracted to the feeling of immediate response to what I do with the ability to take advantage of weaving a champions kit over itself to make everything work perfectly and efficiently. The new champions don't fulfill that feeling for me. They're animations are beautiful, but they have too many instances where abilities feel like you have to wait for them to finish and don't have the control of your champion.