But that's the whole point of playing kayn.
You don't play him for the counterjungle, Shaco and Rek'sai are easily better at that
You don't play him to be a tank, since he's just not tanky enough naturally.
You play him because he is a generalist. Need an assassin? go Shadow assassin. Too many tanks? Rhaast will help with that.
His 2 forms have very different playstyles and as such, very different counters.
Shadow assassin has same counters as most other assassins, but his window to kill is much longer thanks to his ultimate.
Rhaast gets shut down by cc and grevious wounds.
He is very generalist, but that's what makes him good. If Rito decided they wanted to separate the two champions, nobody would play them because there are simply better choices for both categories.
TLDR Kayn is a generalist that can specialize in a certain category, and while this is his greatest strength, it is also a weakness you can exploit using the counters mentioned above.