meanwhile

Again your argument is based on "Because I say so!" - and utter nonsense. From wikipedia:

The Coulomb approximation mathematically follows from the assumptions that surfaces are in atomically close contact only over a small fraction of their overall area, that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact), and that the frictional force is proportional to the applied normal force, independently of the contact area

So steel plates, but not rubber tyres! (Because tyres are flexible and under pressure, so they are under "close contact" across the entire patch - which is why tyre pressure matters and lowering it increases grip.) Once again, look at the diagram. Tyre grip is not the simple product of Coulomb friction but of the tyre making contact with the surface and then acting like a series of tiny springs - ie tyre slip. Tyre slip wouldn't exist without coulomb friction, but it is not the same.

If this is still too complicated for you then consider skidding - this is impossible under coulomb friction! Skidding isn't just movement because adhesion limits have been passed, it is the REDUCTION in grip because said limit has been passed. In coulomb friction, this never happens - if you move because force is too great, then braking/cornering force is not reduced. So ABS, turning into a slide, feathering the brakes, etc, would be pointless.

In fact what happens during a skid is that you lose the spring force of the tyre but still have columb friction - which is much lower.