I don't care a lot about dice other than in combat but I do like the framework of a stated system - which necessitates actions using those stats, and the most common way to do it is through rolling dice.
To elaborate, whenever I've played in completely statless MU* I didn't like how wide open they were. Sure, I can make a character who's a telepath but what are his limits? Can he read only surface thoughts? Memories? Influence them? Rewrite them? If he can teleport does knowing the destination matter? Does the distance? is it possible to block teleportation and how effectively?
I don't mean to necessarily extrapolate based on my personal preferences but I think that's how a number of players do it. They play the World of Darkness, for instance, even if they rarely roll for things unless they have to in order to use the common framework for How Powers Work. If you have Obfuscate 3 you know exactly what dots 1-3 do; it won't let you make buildings disappear. So I won't roll for the damn thing every time (or require other people do so), but only when needed; is someone else actively using Auspex at the time my PC sneaks around? Then let's find out what happens.
I'd say one out of maybe ten scenes of mine actually require rolling unless there's a ST present. But when they do, having the option comes very handy, and even when they do the rest of the system is always needed.