It's not the powerband that PD did not get right. It is the coefficient of friction when the tire spins. This is difficult to measure.
For PD to get this right, they have to get a tire to spin (or burn) slowly to spinning fast (or smoking). Then they would have to reverse calculate what the coefficient of friction at each slip ratio then interpolate. Then they would have to do this for racing tires, normal tires, sports tires, for different tire brands, at different temperatures, etc.
The tire actually is the most difficult thing to simulate on a race vehicle. How you simulate tire can make or break a racing/driving simulation. Papyrus' Grand Prix Legends and Nascar series got this right. EA's Need for speed did not.
Tire can easily have over 100 parameters to simulate correctly. 'Changing' parameters that is. Temperature, pressure, compound, tread, camber, deflection (in all directions), rotation inertia, rotation resonance, slip, slip angle, width, height, etc, etc.
Overall, if I give GPL tires a 9/10, I would rate GT3 tires at about 6/10. IMO, temperature, pressure, and wear rate needs to be more realistically defined.