But is the RKE of the wheels significant compared to the translational KE of the car? It might make an instructive exercise to calculate the RKE of e.g. a solid disk of mass M rotating with angular speed ω = v/R where v is the linear speed of the car and R is the radius of the wheel.
For some old diesel engines, the RKE of the flywheel could be significant, too. If you ran the engine at full speed, with the car stationary and then lifted the valves and let the clutch in, the car would move forward at 'significant speed', implying that the RKE of the flywheel could be significant at low car speeds.
I can't do that experiment with my 3.5 ton boat because I can only engage drive with the engine on tick over but, as KE is proportional to v2 and the maximum speed is less than 10 km/hr, the flywheel energy must be significant. I must do the sums one day.
They used to quote the instantaneous horse power of traction engines for when you would use the flywheel to provide some high power in bursts.