[TheKeeg]

This is a difficult question to answer, but I can try to shed some light.
There is a difference between friction and traction; friction is the resistive force to motion while traction is putting friction to use. (it is mostly semantics, however.)

Adding wheels or increasing wheel thickness really does two things. Like you said it increases the life of the tread, but that is not the whole answer. The amount of horizontal force that you can produce with a given coefficient of friction does in fact increase as the normal force increases, however it does so at a diminishing rate, i.e., it is not a linear relationship. For this reason, wider tread is more efficient because the relationship between normal force and frictional force is more linear.

Also, think of the grooves in your tread as teeth and the carpet as another set of teeth. As your wheels try to spin the teeth on the wheels will dig in and push against the teeth in the carpet which will move the robot. So the more teeth you have pushing against each other, the more "traction" you have. Lets say there is only one set of teeth, i.e., one groove in the tread and one in the carpet. Now, since the tread is a compressible material, it will not take much load to deform the tread and cause it to slip. If there were 100 pairs of teeth it would take a lot more to deform all of the teeth and slip the wheel.

Hope to makes sense.