Let's take a step back and examine why we would use horse-stall mat, neoprene, Kraton etc. in the first place.
There's no question that those materials are "grippy"... generally touted as somewhat easier to hold onto when the handle is wet or greasy, than G10 or micarta.
But in my experience, the difference in "grippiness" is over-rated if the handle is designed well in the first place, and really doesn't make much difference at all if the handle is in fact wet or greasy. For instance, a poorly-shaped Kraton handle (I'm thinking of the stock CS TrailMaster in particular) will absolutely want to fly out of your hand if you use it in a driving rain for heavy chopping.
But! you may say, a rubbery handle can be deeply checkered... that makes no difference at all, because other synthetics and natural materials can also be checkered/textured. The TM handle I spoke of was nicely-checkered, and that was absolutely no help.
Soft materials can be obviously be squeezed harder by the user, adding to control and "gription". But I defer to noted designer Ethan Becker, who famously said (I'm paraphrasing here) "If you have to go to a soft handle material, maybe you're not done designing your handle yet."
I discussed this very topic with Mr. Becker at his Gathering a few weeks ago; neither of us could remember his exact original quote at the time, but he agreed that we had the jist of it.
My point is, if you have to really squeeze the handle to hold onto the knife in use, it's a very poor design. If the dang thing hurts your hand when you use it, it's bad. If it wants to slip out of your grasp in exuberant use, it's bad.
If you don't have to think much about holding onto the handle, and can use it comfortably without much thought or effort, and it doesn't hurt or cause blisters, it's a very good handle design. I'm convinced that geometry plays a far greater role than materials.
If you're relying on shock-absorption to make a knife more comfortable and efficient to use, you're just fooling yourself. If a cutting implement feels like a brick or sends pain up your wrist/arm when you use it hard, it's a poor design. No matter what you make the handle out of, that's not going to change.
There may be extreme examples, like competition cutters (where horse-stall mat is very popular as a handle material) that may transcend these basic concepts. I remain to be convinced of that, and I'm very interested to hear more about it.