Waves is like an endless living changing skate bowl park, halfpipemekka - just MUCH more fun !
And it even changes every day, sometimes every minute
On a waveboard it is NOT the closest thing you can come to surfing.
It is sooo much better and more options and possibilities - the feel is just way better than surfing IMO
Other times surfing is better - but they are two very different things in my eyes, and should not be compared...
If I wanted to surf (if good waves), I would take my surfboards instead of a kite
So to compare with surfing is to degrade kitesurfing in waves
As all the others have said - you got endless options, because the water is more flat between the waves than even flat water can offer, and you still got the dynamic "living" wave that can change instantly and always offer a challenge or simply "good feel".
Even knee high waves are a pleasure to "slash" when you hit the curl just perfect in sideshore wind and just before it breaks
Other times in bigger waves, you just park the kite, let go of the bar, and enjoy the ride "down" for a moment
When you have ridden many years and many waves, on waveboards - you will typically not jump much, only occasionally - because it IS fun, but not nearly the same feeling as when you nail a perfect timed bottom turn and horisontally going up in the curl when the wave is about to break - so you get "spit out" and maybe goes aerial, maybe not, and can make fluid powerful connected turns - this very "feel" is what we all seek again and again, and hardly never gets boring
For the spectator, it is odd, as we all seem to do the same thing over and over - so I understand the question "What do people like about kiting in waves ?".
And we can try to express our feelings in text here, but you will only know what it is that we can not resist and why we chase waves all over the world, when you get "hooked" on waves yourself.
So the answer to your question could just as well be: You have to feel it yourself in order to know !
As it IS a truly very very different world, different gear (boards and kites are different) and different riding techniques.