Most accidents occur at less than 40 mph; if "dozens of meters" equates to about 100 ft, that represents about 1.7 seconds at 40 mph. Assuming a coefficient of friction of 0.8, it is theoretically possible for a car traveling at 40 mph to stop in 67 ft; call it roughly 70 ft. If the system can apply the brakes within 500 ms, that's enough to be useful, although clearly it can't stop you from plowing into a car stopped in the fast lane of the highway.
Speaking of highways, the only reason people can manage to drive on highways is that the things you're most likely to hit are traveling in the same direction; if they were slaloming between stationary obstacles at 60 mph most drivers would be dead, fast. What makes highway driving safe is that the closing speed between vehicles is usually modest; usually on less than ten fifteen miles per hour. So actually the system might have more effect on the highway so long as speed discrepancies are in the normal range.