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Electric to be

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I have been led to believe that for a car initially traveling at some constant speed: the torque at the axle of a wheel will be equal to the torque caused by static friction at the point of contact of the wheel. This is true so that the wheel doesn't angularly accelerate and so the point of contact does not slip with the road.

Now that's all well and good. However, before the axle provided a torque, the car was traveling at a speed v = w/r, which satisfied the no slip condition. However, afterwards the static friction force applied at the wheel speeds the car up (while maintaining angular velocity w). Now v is larger than the initial w/r, so the car must slip, right?

So didn't this initial process that was meant to stop the car from slipping, cause it to anyway?

I'm somewhat confused.