Physical question: why wide tires?

Hello together it is often talked about that one can brake and accelerate better with wider tires and drive faster through the curves. I thought about this and can’t quite explain why this should be so, because the formula for the friction force that can be transmitted is FR = [coefficient of friction]*[normal force] and neither the coefficient of friction nor the normal force depend on the rise surface. I can imagine these 3 possibilities at the moment. 1) Wide tires do not improve the braking distance etc. at all, as is always claimed, but simply have less wear and look good 2) It is not the transferable friction force, which represents the essential size for the above mentioned disciplines 3) The above formula is simplified school physics and the force actually calculates more complicated and also depends on the surface (does I think unlikely…) Maybe everything is also wrong, I hope someone has here more de A look through and can enlighten me! Greetings James B.