I honestly hope Riot nerfs Kayn. I've played him in a handful of games, and as someone that prefers his Shadow Assassin form, I feel like he's way too strong of a lethality assassin.
His Q, despite having terrible ratios, hits twice. If you flash all in someone level 2, you get the double proc (which from base damage is like 110 damage rank 1), the W (which has stupid good damage/scaling and level one also hits for 110 before armor) so you're at a Talon level of burst damage with a level 2 all-in.
Beyond that level 2 powerspike, he does get dumpstered by a lot of champions for levels 3-5 or so, but it happens. There are some champs that spike hard, then fall then come back. At level 6 though, you have the outplay potential to dodge out a LOT of potential damage as well as stick to your enemy so they can't escape. His ult lacks damage because it's more of a utility anyways. I've seen a few comparisons to Taliyah where "No one knew how to play her, then they buffed her, then it went down hill from there." and that's exactly what will happen with Kayne.
Once he transforms, his poke damage is ridiculous (remember, I use the Shadow Assassin form). His W has extended range, he can move while casting, and he gets the 27% bonus Magic damage on top of the high physical damage and that magic damage passive only has like a 9 seconds cooldown ... so everytime your W is off cooldown, you can literally just poke someone for 400 damage while still being out of any harass range... as a melee assassin... at around level 11 after having 1/1.5 items completed...
Just for some reference, I played him the other day on Twisted Treeline ... literally 100 to 0 Lee Sin/Orianna instantly with no counterplay potential unless they flashed away from my Q. I feel like people build him like a Bruiser and expect assassin level damage, but these one shots were happening with Warrior jg item and Duskblade (and yes, duskblade is SUPER OP right now but that's a different story).
Now, take everything I say with a grain of salt because I was playing with lower ranked friends as a Diamond player, but he has so much powerfarm and gank potential as well.
If you read the small print on his Q, it does bonus damage to minions. On Twisted Treeline, I could clear all 3 camps with no leash and one refillable without smiting... granted, I did smite so that I could immediately gank, but there are several champions that can't even do that.
Furthermore, be it in lane or in jungle, "Let me walk through a wall and heal 100 health rank 1" ... did I mention he could casually walk through walls? You have Zac level gank routes, and if you're like me and go Shadow Assassin, you get 70% bonus movespeed AND slow immunity while running through terrain... Balanced?
I even did a 1v1 top lane Kayn vs Renekton. Level 2, I heavily out-traded, forced a TP, and had an edge in lane. Renekton proceeds to hit level 3 and way out-trade me and even pick up first blood. I hit level 6, instantly kill him, then every death I had after that was me testing the limits of Kayn with diving and seeing how turret agro works. If you can burst a Ninja Tabi's rene that's sitting at 2.7k for 80% of his health bar ... in BRUISER form (without that extra nearly 30% magic damage), then something's not right.
So yes, his early game is weak and his ult doesn't do much damage on its own, but it's a mobility ult meant to make it impossible to peel you off of your target. It's not an Urgot Execute. When he hits his powerspikes, he'll win every trade so long as you don't completely whiff everything.
As I mentioned before, do take everything I say with a grain of salt because I haven't played him in ranked in Diamond, but it doesn't feel like Kayn needs a buff. The people that do understand him have high winrates. Kayn's winrate across everyone is like 39% (looking at op.gg), but the people in diamond/masters that have the most games on him (9-14 games since he was JUST released), have MUCH higher winrates. The LOWEST was 45%, but Sinykul (D2) has a 64% winrate across 14 games, Felfire (D2) 56% winrate across 9 games, Danwel (D1 in promos to Masters) 56% winrate across 9 games. Odds are, these winrates are on the low end because KAYN WAS JUST RELEASED. They were still learning the guy as they played him in ranked. Sinykul has a 64% Winrate across 14 games, but if you look at his last 10 games, 80% winrate.