I'll have to admit, the intuition for why friction is independent of contact area has always eluded me. If you think of a tire contact area that is one atom wide, it's hard to believe that that generates as much friction as a contact area a foot wide. Maybe that's because we know intuitively that the one-atom wide contact area will not be robust enough to survive the contact. So it's probably a good thing that I didn't become a physicist.