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While there is no area in the friction equation, in the real world it is nonetheless a factor. You got to remember that a larger area makes it so small patches of lower friction (sand patch or water or trash or whatever) have less of an impact, with more area you have a higher chance to still be in contact with the asphalt. More area also gives more opportunity for the ridges in tires to displace water or grip onto gravel/dirt. While simple contact friction is the same, total friction is not necessarily depending on the conditions.
Responding to:
However,
Unless we're talking about liters of sand/gravel then this fails to explain how motorcycles have as much grip as cars do, as is evidenced by cornering ability.
Tread depth and pattern handle these.
...
Racing tires are wider because they need to handle higher loads. Racing slicks also maximize contact area to extend tire life and reduce wall thickness. There's thermal conduction as well. Rubber is an insulator. Rubber friction changes with temperature. So does modulus, leading to more deformation and thus more heating. Too thick rubber makes a hot tire that loses friction coefficient. Too thin and it wears too fast, you're on steel 3 laps in. so you make it wide enough to distribute the load, reduce stress, and control heating while trading off mass. This is also controlled by chemical composition. After that you're designing for weather conditions.
Passenger vehicle tires focus more on climate and adverse road conditions and long life. Because they are much lower performance, they have much lower loads and use tires with less contact area. The same is the case for motorcycles and bicycles.
There's no space for thread pattern if the area is too small.
This is perhaps an easier to understand explanation:
https://www.physlink.com/Education/Askexperts/ae140.cfm