Unsprung weight, is an agility killer.
The more weight a car has on the corners, the worse a car reacts on turns.
Reducing wheel weight, brake weight and other weight on the corners of a car (also sprung weight) does make sense.
Also, unsprung weight is "bad", because of mass inertia. (manufacturers try compensating that with "intelligent" suspension systems.)
Just have a look, how fast cars are built (also fast around corners

):
- As much weight as possible in the center of the car. (Driver, engine, gear box)
- lightweight brakes (carbon)
- lightweight wheels/tires
If you now have a car where the suspension system has a setup for "high" unsprung weight and you reduce a lot of unsprung weight, it could be, that the suspension is to hard, causing the car to "jump".
A suspenison system is a "system" that needs to be setup to various conditions, like car mass, but also road conditions.