I actually work for a tire company, but we don't make ATV tires here.
We do make some pretty awesome off-road tires, including for the Stryker fighting vehicle and Canadian LAV.
Weight, tire pressure and overall diameter are important on these machines.
I am a fine one to talk, I have 22" tires on my machine right now, too tall. The lower the tire the more stable it will be.
I needed the clearance for a little mud bashing. Not that that is over I will be back to lower, lighter tires.
Thick heavy tires are not the way to go. Lightly constructed tires swing easier, eat less horsepower, and grip better.
They conform to the ground and rocks and grab like a hand and fingers.
Thicker tires bow and buckle up in the middle losing grip, even if the air pressure is low.
Better tires have sidewall protection built in without making the sidewall heavy, stiff or thick.
Proper air pressure is critical to get the tire working. Too much and it bounces over the bumps. Too little and it can pinch against the wheel and pop off the rim. A flat profile tire should ride flat even on a hard surface. If you can see light under the sides, it is over inflated. About 3-5 psi on a Blaster. It takes a special low pressure tire gauge to read it accurately. The rounded profile tire should still be using half of its width on flat surfaces at about the same pressure.
As for avoiding flats, that has everything to do with air pressure too. Too much or too little and a tire is easy to puncture with something sharp or pinching against the inside of the rim. With just the right low pressure a sharp stick has nothing to work against and has to intrude 4-5" to hit the rim.
So, 20-10-8 flat profile sounds great. 6 ply? Maybe too heavy. Thick sidewall? Not my first choice. Remember, 3-5psi.