The design of a spring affects how well the vehicle will ride and handle. A spring that absorbs lots of energy will generally offer a comfortable ride. But there are always engineering trade-offs. This kind of spring generally requires a higher vehicle ride height, which will cause the vehicle to feel unstable during cornering. This rolling is called weight transfer, and it is caused by centrifugal force acting on the weight of the vehicle as it goes around a corner.
Weight transfer can overload a tire's grip, which ultimately hurts traction, and therefore handling.
The other main part of a car's suspension is the shock absorber. Contrary to its name, a shock absorber plays a minimal role in absorbing impacts taken by the suspension. That's the spring's job. A shock absorber dampens road impacts by converting the up and down oscillations of the spring into thermal energy. Without a shock absorber, a spring that has absorbed energy will release it by oscillating at an uncontrolled rate.