the formula is mega simplified and doesn't really apply for elastic materials, and definitely not over rough surfaces. at the road level it's not just friction involved. there's mechanical engagement with the peaks in the asphalt, and more are better. so for tires, this discussion is fail.
for brake pads, well.. also fail, as someone else mentioned the surface area comes in when you're talking heat dissipation. friction is temperature dependent.
only reason you'll ever wanna cut back on tire and brake surface area are for other performance losses associated with big, unsprung, spinning parts.