Imagine holding a bent over squat position for hours. With beam suspension, the rider learns to relax through the rough spots, giving the low back and legs more energy to go faster and farther. At the end of the ride, the legs are more ready to run. Without suspension, the car would spend a good deal of time in the air or at least have very little pressure on the tires. A tire that is not pressed against the road cannot hold turns.
Crashes tend to result.
Imagine pulling a toy wagon along a rough road while you run. It bounces over every little bump. If you try to run around a corner pulling the wagon, it flies out from the corner. Now watch a car go around a corner on a rough road. The wheels move up and down but stay in contact.