On a street car, a lightened flywheel will mostly affect idle, clutch engagement, and revving the engine in neutral. The first two negatively.
Yes, reducing rotating mass that needs to be accelerated helps to increase the rate of acceleration BUT the mass that needs to be accelerated also includes transmission internals, diff, half shafts, axles, drums/discs and wheel assemblies. The greater the diameter, and further out on the diameter that mass is located, the greater the effect. Obviously where you can spend money to the most effect is tires and rims.
I have run lightened flywheels on my hopped up bikes/scooters. There the flywheel is a much more significant percentage of the total mass to be accelerated. Yup, they are more responsive. But responsive both ways. In other words they also respond quicker to negative inputs like hills and winds. And, yes, they are ridiculously easy to stall.
I do not feel a lightened flywheel is worthwhile on a street car. Spend the money elsewhere.
YMMV