On car tires, shoes and other such items, having less of the material in contact with the surface underneath increases traction. Why is that? Isn’t friction a function of the contacting area and speed?
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Under ideal conditions maximizing surface area will help traction. This is why for example drag racing tires are smooth. So in that sense your intuition is correct.
But think about things that can cause that ideal to not work out. Suppose you have small balls between the two flat surfaces, that is going to result in much lower friction because the surfaces don’t get to touch! Perfectly flat shoes on perfectly flat floor would be great traction as long as the floor is perfectly clean, but add a little sand or grit and suddenly it isn’t good at all.
Similarly if the surface being walked on isn’t perfectly flat then a flat shoe won’t make good contact. By adding gaps in the shoe surface there is somewhere for debris to be pushed aside and space for the shoe material to deform to match the surface.
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