Mostly it harms the handling and safety. Remember: the job of
the suspension is to keep the tires on the road so that you can
keep the rear end from trying to pass the front end. IOW, if
the tires aren't on the road, you can't control of your car.

If you have different damping rates on left/right, the car
isn't going to want to go straight while braking or
accellerating on bumpy surfaces.  Once the shocks are gone,
it's also going to be very jittery and hard to control on bumpy
curves.

You're already seeing it--there hasn't been anything left for the past
20,000 miles or so. They've shuffled off their mortal coils, run down
the curtain, and joined the bleedin' choir invisible.

Worst case, in an emergency your stopping distance may be about 30%
longer than with good shocks. Or worse, if you're not good at threshold
braking.