OP – you haven’t gotten your answer yet. If you asked “why are street tires grooved”, then everyone giving the “rain” answer would be right. But, you asked why “street tires with no tread are slippery”.
Little background – tires are made from rubber and plastic compounds. These compounds are heat sensitive. If you overheat them, they will change their chemical compound. Usually, this means that they get very greasy when hot, then get harder than original when they cool. Even warming and cooling normally several thousand times will harden a tire.
So, a street tire that has naturally worn all of its tread off is going to be VERY hard. Think about what would happen if you put hard plastic wheels (like on a kids’ Power Wheels toy) on your car. However, if you take a brand new street tire and mechanically shave off the tread, then it’ll be VERY grippy! In fact, it’ll handle better than a new, non-shaved tire!
Also, F1 tires have a MUCH softer, grippier rubber compound than street tires. You can literally stick your fingernail into an F1 (or other racing slick) tire and leave an indentation of your nail. This is why a slick F1 tire is more grippy than a slick street tire (even one that’s been shaved).
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