Actually, I dont think there is many "general" traits about a wave kite !
One of the things in common everybody lists, is "good drifter".
But this is not a wavespecific desire IMO, but a general thing EVERYONE wants.
Freestylers, having slack lines in handlepasses, but also sometimes riding with speed in the landing towards the kite - also want a kite that just drifts back and is easy to recover.
Freeriders, sometimes make mistakes and the lines unintentionally go slack.
They want a kite that just sits and balances, till the lines are tight again.
Remember the "good old" C kites in the early days ?
Well, good and good - they would hindenburg before you could blink with your eyes
Look at the C kites nowadays ?
They drift simply awesome, and for some used as wavekites too - a HUGE difference, simply by good kitedesign and balance
So I dont see this as a specific wave related feature, simply evolution on all kites.
The only real thing that is wavespecific, I think, is the ability to turn while depowered
In freestyle this feature is not that important - but for waveriding it is essential !
All other parameters are extremely individual IMO, and goes both ways, regarding waveriding :
1. Some like a tad smaller kites with lots of power.
Others like kites with lots of depower and no powerspikes.
2. Some like kites that sits deep in the window.
Others like kites that flies fast across the window and sits further forward.
3. Some like a kite with a constant predictable pull through turns (C kite like).
Others like a kite that can be turned without pulling whatsoever (pivot turn like).
4. Some like kites with lots of bar pressure (feedback)
Others like kites that can be easily turned with one hand (low bar pressure)
5. Some like kites that can be relaunched fast, typically low AR.
Others dont care that much, compared to other advantages of slightly higher AR.
6. Some like a kite with an easy depower stroke that is very continous and easy/natural.
Others like a kite that can be depowered on a VERY short stroke immediately, like an F1 gas pedal.
Of course, everybody wants a "fast turning" kite too, but somehow this is also an evolution, AND a compromise, as if you want a kite that flies fast across and goes upwind, it is slower turning, and reverse.