I would think after any regular use at all in muddy/sandy caves the reasons not to use an ATC with 10.5 or 11 mil caving rope would be obvious. Wear, "stuffability", etc. Everything that's already been mentioned. I used my ATC in a multi-drop cave trip ONCE because we were hauling around a lot of rope and survey crap, even though none of the drops were that deep at all. I wanted to be as light as possible. I didn't have a Stop then so it was a full size 6 bar, my climbing ATC, or a Münter. Started to turn the edges on my ATC into knife blades. And I had to get a new ATC after than trip for climbing.
While I personally think a tube style device superior to a figure 8, I won't get back on my "I hate the 8" horse. I'd still like to see a tube style device made for caving though, with the openings more suited to dirty 11 mil static rope, and probably made out of steel itself. You probably wouldn't really save that much weight over a stop, but I imagine it would be cheaper to produce/buy, and have applications in pull down trips and canyoneering. Something designed like a BD ATC XP to reduce the edging that I've seen on regular ATC's, sold as a package deal with something like a Petzl Freino for additional friction options. (See pictures below).
Petzl's Pirana made a stab at this, but the reason why I don't own one is because I don't like the twist an 8 puts in the rope. I think a tube style device designed for caving with someway to have a little variable friction would be better. But no one's made one yet. I guy can dream though, right?