Why does friction increase when speed does?

Answer 1

There are several types of friction involved and the whole question comes down to energy and where it goes.

I will only address a few types.

The air resists the car moving through it, the faster you go the more energy it takes to push the air away then more energy is lost as speed rises because the car creates a low pressure and turbulence area behind it. Third is the air actually sliding over the body. All of this increases "friction"

Rolling resistance of the tires is cause because the tires "flex" as they roll (the bulge on the bottom when you are parked) the faster you go the more they flex the more energy they use.

All the mechanical bits in the car slide past one another, the faster they go the more energy it takes.

Answer 2

Friction increases with speed because at higher speeds, there are more interactions between the surfaces of objects, leading to greater resistance as they move against each other. This increased interaction generates more heat and wear, resulting in higher friction forces.