Friction is necessary between wheels and the ground in order to prevent the wheels slipping. Static friction doesn't oppose motion, but rolling friction can do so.
In the case of a wheel driving a vehicle, if the driving torque of the wheel turning clockwise is T and the wheel's radius is r, this results in a couple. So there's a force at the point of contact of the wheel and ground of F = T/r acting backwards and F = T/r acting forwards on the axle. If there's no slippage, a balancing force F = T/R acts forwards at the point of contact on the ground. So these forces are in balance. The other unbalanced force at the axle pushes the vehicle forwards.