They have major differences in the kits.
Shadow Assassin has 0 hard CC. No useful dash. (its actually faster to walk as long as you have T2 boots and a cloud drake) and his only form of flanking or getting out is on a 13 second cooldown. So once he is in he is pretty much in.
Elise. Hard CC. and Id honestly say that rappel is a better ability than shadow step in every situation except flanking. So she gives up a bit of her on command burst to be able to stun someone for 2 seconds.
Ahri is a kite mage. Not a burst mage. She was a burst mage a long fucking time ago. (RIP DeathFire Grasp)
LB isnt a burst mage. she is somewhere in the middle of a kite mage and a burst mage, but doesnt fully commit to either.
You havent really put up any AP champs that have comparable kit styles.
Now a real burst mage like Viktor. He can 100-0 people faster than a kayn. and has more reliable AOE. He is ranged so he can stay at a distance while doing it. Viktor has Hard CC and that hard CC is basically a mini Orianna ult. While less reliable still works the same way.
Kassadin. Even more AOE than Kayn with his Ult and E. while having a fuck load more mobility. gives up a little bit of damage for it.
Annie. We have all seen the 2/2/2 Annie mid who while not fed can still 100-0 an entire team alone.
What have we learned. Kayn has a tradeoff of no hard CC for damage but that still doesnt mean that there aren't mages that kind of do his job better.