You are right that more surface area tends to mean more friction.
Textured surfaces have more surface area than flatter ones. Imagine a straight line from point A to point B versus a “textured” line that zig zags and curves around on its way from A to B?
Which line is longer? The “textured” line is. If you bring this example into the third dimension, you can see why a textured surface has more surface area than a flatter one
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