larger diamter wheels are exlusively to clear brakes.
it a car at the track had brakes small enough to run 15s (and still have enough cooling to the rotors), they would. Nascar wheels are all 15", most rally cars run 15". F1 car wheels are ~11"
15" wheels and tires have much lower rotational inertia (which affects accelration and braking, like a flywheel). this benefit, plus lower mass outright, out weighs any sidewall squirm issues.
the ONLY other reason to go to a larger diameter wheel is tire choice. for example. in 15" there is no choice in tire width between 225 and 275, so if you want 235, 245, 255, or 265 wide, you must go to a different wheel size (17" being a convenient size to find all of those).
for auto-x: '04 Liquid Grey ZX3
for street: '02 Infrared SVT