Can somebody explain why rolling resistance does not depend on the
Rolling resistance is due to inelastic deformation of the tire. It's just a guess, but I would think deformation of the tire material would primarily occur normal (perpendicular) to the contact surface between the tire and the road due to the weight of the vehicle.
Any significant deformation of the tire parallel to the contact surface in the direction of the motion of the vehicle would probably occur only during acceleration and braking of the vehicle. as opposed to while the tires rotate at constant angular velocity.
I should add, according to Wikipedia, although the equation for rolling resistance doesn’t explicitly show factors such as speed, torque etc, those factors are built into the coefficient of rolling resistance.
You may be interested to know that the Society of Automotive Engineers (SAE) model for rolling resistance in SAE J2452 includes vehicle speed. The equation is
Rolling Resistance ( N / Lbs) = P$^α$ Z$^β$ (a + bV + cV$^2$)
P is the tire inflation pressure ( kPa / psi)
Z is the applied load for vehicle weight ( N /Lbs)
V is the vehicle speed ( km/h / mph)
alpha, beta, a, b, c are the coefficients for the model.
The units of the coefficients are matched to the units used in the model, i.e. ( metric / Imperial)
Hope this helps.