An infinitely rigid wheel that provides no suspension at all cannot impulse a car.
The only way for a car to move forward is if you develop a differential grip in the wheel. You can read here:
That infinitely rigid wheel would also give you no steering at all.
Of course, that would solve the problem of comfort and make engines unnecessary, as the car wouldn't move at all.
Triple play: you would have terrible handling and no acceleration at all, but at least you would look stupid.
Wait...