Ground clearance comes from tire size, so a bigger tire means the axel is higher, allowing you better angles and more ability to get over obstacles. As for the tread, the benefit is so that it has less likelihood to slip sideways when angled on wet surfaces. Think if you are angled left/right in mud or slippery rocks, having better tires helps if only just a little. If you look at the non-offroad versions, typically the tires are set for gas mileage and tend to be small in diameter, skinny and without tread, thus more likely to sink in mud, slide on the trail, and have lower ground clearance over obstacles. Also offroad tires tend to be a bit more puncture resistant. My trailer also has electric brakes that sync with the vehicle, so if I'm coming up or down a muddy trail, it's nice that both my truck and the trailer have traction to stop. Having a truck stopped but the trailer sliding forward or sideways would be bad.
I don't think it has to be the world's best offroad tire, but I can see how there are benefits.