[big1boom]

Wider tread provides absolutely no benefit. When the surfaces are hard, uniform, and flat (Lunacy)

A wider tread does increase the amount of gripping ability when you are talking about carpet though. Think of carpet wheels kinda like Velcro, when you drive a carpet wheel over carpet, some amount of interweaving occurs, resulting in some amount of grip based on contact area.

Whether or not the amount of increased grip is usable is still up in the air, but I am betting that it would increase grip a small amount.