This video shows a driving test comparison. One car has driven 80,000km and still has the original shock absorbers, the other has brand new KYB shock absorbers.
The vehicles complete a slalom test (you can see it in slow motion) and an emergency braking test, to compare the difference in performance. It's clear to see how much more responsive the vehicle with new shock absorbers is.
With worn shock absorbers, your steering / handling is compromised and your stopping distance is longer - that's the difference between stopping safely and hitting a hazard.
KYB recommends replacing shock absorbers and suspension mounting kits after 80,000km.