Bicycles are limited to the power of the rider, so to make them faster you reduce resistance by using narrower, high pressure tyres and making it more aerodynamic.
Fast cars have plenty of power, and are limited in how fast they can (safely) drive by how much grip they have – put 1000hp in a car on tiny tyres and it can drive fast, but will wheelspin when accelerating and skid when braking or cornering. Fat tyres give more contact area with the ground which improves grip.
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