I'm pretty new to knives, but I had some very bad experiences with stabilization in musical instruments. That was quite a few years ago when stabilization seemed to be more of a specialty than the norm.
I got a piece or two of figured maple that had just had the life taken out of it, same with a piece of curly koa. It seemed like anything with a really fine, silky smooth grain was susceptible.
I picked up a piece of curly stabilized redwood at Tru-Grit, and it was absolutely beautiful, the stabilization didn't kill the figure at all. I was all excited about it, but they didn't seem to be particularly impressed. I think that the newer stabilization products and more refined methods are getting much better results. I remember that it used to be essentially a crapshoot if you were going to get a cloudy piece of wood.
Wenge is one I would never want stabilized, as it is one of the few woods I've encountered that can pretty much be finished raw with a clean buff, and come out great.