When you modify their braking behavior, is that enough to improve their overall driving behavior? Or do forward collisions and rear-enders make up substantially all of what the driver can control, so training the behaviors to reduce that type of near-miss reduces the driver's overall crash risk? To the point that it's similar to the safest tranche?
Is it that hard braking events are broadly indicative of surprises of lots of sorts, and so it happens that the only way to eliminate them all is to develop a full range of defensive driving habits?
More Goodhart's Law or Serenity Prayer?
Regardless of everything else, forward collisions are most likely to have the driver considered at-fault. Seems like reducing those in your insured population would reduce covered losses more than reducing collisions where your insured may not be at fault.