When a tire is pushed to the limit rubber tears off the tire. The more
rubber in contact with the road, the bigger the piece of rubber that has
to shear so the greater the force. It is really very different than sliding
hard rigid objects. The more the surface of the tire is cut up into little
blocks with tread, the more the blocks distort under stress and the poorer
their contact with the road. For this reason performance highway tires
are made with bigger blocks of tread. The up side is better performance on
clean dry roads. The down side is poorer performance on dirty, wet, snowy,
or icy roads. Race tires just carry this concept to the limit and some are
made with no tread at all.
There are several mechanisms for slip and the rules for friction commonly
given in Physics texts are pretty accurate for some of these mechanisms and
pretty inaccurate for others. They generally work well for hard rigid objects
sliding without lubrication. They generally don't work well for soft objects
or lubricated objects.