You should see what damage an overloaded logging truck causes...
Most of it is due to the visco-elastic nature of asphalt. Deform it enough and it comes to a point where it tears instead of rebounding when the load is removed. That kind of deformation is permanent. A car doesn't have the mass to cause that much displacement.
A lot of places charge trucks based on a fee per axle. Which makes truckers want to overload their trucks to keep their costs down. A ground pressure fee would be a lot better but it's a lot harder to figure then counting axles.