To my knowledge this is all correct (and the snipped out parts also) and a materials properties do change with temperature including the coefficient of friction. But a small quibble - the shape and irregularities changing "grip" do not alter the coefficient of static friction. Basically the tire can lose contact (leading to no friction or sliding friction) and wider in the direction of force reduces that. (added, I think that vibrations can also impact it in a similar manner)

(Before anyone jumps all over that out of context, I alluded to this when I first brought it up. And also sought to exclude racing tires from the comparison. It's kind of obvious that racing tires or a performance sports car will better the bicycle.)

In the context of car vs bicycle, it means that while there are a lot of reasons why the wide tires with large contact patches are desirable, and many of those reasons relate to traction and cornering, it is a mistake to say that a four wheeled vehicle will have an advantage simply because there are four contact patches, or wider contact patches. The advantage of these contact patches is that they're associated with the racing tire.