Dual compound tires are already on the market....softer tread compound and tougher sidewall compound.
The edges make a lot of difference in how a tire bites, whether it's snow, dirt, or rocks. The tires that bite the best have a combination of soft compound and a lot of edges. Swampers have a soft compound, but not enough edges, and so don't make the best rock tires. Grooving them improves their performance, because it creates more edges. More rock crawlers are getting their tires siped, and it's generally agreed that the increased number of edges improves performance on the rocks just like it does on wet surfaces.
The MT/R came out and very quickly became the tire of choice for competitions and for recreational rock crawlers. This tire has a reasonably soft compound and a lot of edges, plus big enough lugs to grab irregularities and ledges. The new Krawlers are the tire of choice now, mostly because the competion versions have such a soft compound.....too soft to run on the street. It's yet to be seen if the street version will perform better than the MT/R.
Another element involved in tires for rockcrawling is side grip, or side slip. A tire needs to be able to hold you on a line, and not let you slip off of a narrow edge or ridge. Certain tires on the market are bad in this area, like the Baja Claw, because it has a limited number of grooves longitudinally around the tire. A slick tire would be really lousy in this area.
The big lugs on a tire help to grab and push on steep surfaces, like on irregular waterfalls (most are) and on big ledges. On normal rock gardens you can't tell much of a difference between the MT's and the AT's, but when you get to the big ledges and climbs the MT's have a clear advantage. This isn't theory, mind you, it's observation and experience.
Additionally, we do encounter water and mud when rockcrawling. We cross creeks, go through water puddles, and sometimes it even rains on us. In the real world a slick tire just won't work, for MANY reasons. The only thing a slick would have going for it is the soft compound, but there are too many situations where that just wouldn't be enough.