Although with careful use, acrylic won't melt, it doesn't hold heat. So it really doesn't protect anything on the other side of the hot pan. Both cotton and wool do absorb the heat thus protecting the hand or the table top.
Acrylic will melt and cause worse burns if it comes in contact with the skin, while although cotton and wool will burn, it's really rather hard to burn the up without continuous application of a heat source, IOW, they need to be in the flame. Once removed, cotton may slowly extinguish itself, and wool generally always does. That's why cooks helpers, in the times when cooking was done on an open fire, wore wool aprons. The sparks would land on the wool and then die out. Lots of little holes on the aprons, but very little chance of the made burning up.