The area of contact is why this this whole thread was brought up in the first place. The original question was that if friction is independent of surface area, which we all agree it is, then why do wider tires grip better?
I've thought about this a little more and have some more ideas on the subject.
In a lot of physics examples they are done under perfect conditions. The ones I gave above are such examples. e.g. A feather will fall as fast as a lead weight, but only if there is no air resistence. My examples assume that the property of the rubber doesn't change with compression of the rubber. I don't believe that is the case. There are also shearing forces as well as heat to deal with. Using wider rubber allows shearing force to be less. It also allows there to be less compression of the rubber which probably maintains the rubber's coefficient of friction.
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351W 89 Mustang GT Convertible