Simple physics dictates that the friction force is equal to the normal force times the coefficient of friction. Nowhere is the contact area involved in the calculation of friction force. Look it up in any physics book and that’s what you’ll see. In my initial (incorrect) calculations I factored in the contact area by saying that the contact area would determine the force applied by the hydraulic system when in fact it’s the cross section of the brake piston that determines the force applied. However that’s not to say that in real life the contact area plays no part on friction. It’s a proven fact that wider tires give better traction. Theoretical physics and real life don’t always mesh perfectly.

-J