When driving, you want to keep your velocity relative to other cars as low as possible, while retaining your ability to avoid obstacles / not murder cyclists and pedestrians.
If cars could go at mach 3, then you'd want to avoid roads entirely: it's not feasible to avoid obstacles at that speed, and you certainly don't want to get hit by shockwaves or – worse – actual cars travelling at such relative velocities. So no, you would have worse problems in this hypothetical.
