Hi so i know this is nearly a year late and you probably dont care anymore but the reason race tyres are smooth is to reduce friction so they can go faster. Normal cars have them so we can break quicker and to reduce the chance of slipping on icy or wet roads but race cars dont need that as they are not for everyday use so they dont have these ridges meaning they can go faster although more dangerously. If you still care, i hope that helped. Also, i have no idea about the eggs, that seems like something that shall remain a mystery
Regarding the paragraph for friction I believe that they missed something incredibly important.
Assuming equal weight (force), decreased Surface area by the fingerprints relates to increased contact pressure! Increased relative contact pressure would increase the variations in contact pressure between two neighboring points. Perhaps this is written in one of their scientific papers somewhere else but I believe this should be studied. That increased contact pressure at variable increments (over each of the fingerprint ridges) would allow for efficient tactile perception as variable pressure would be easier to detect in finite incremental segments, like pixels.
Please reach out to me/credit me/comment below if you’re interested to speak further on the subject.