I agree it would take a longer time to fall and bounce 10 ft , but a climber-like object in free fall will take about 0.6 sec to fall 10 ft. Jump off a 10 ft high ladder. In ~0.6 sec you will hit the ground.
I'll have to think about this, as there are two antagonistic factors. A shorter fall means a lower terminal velocity, but a shorter rope means higher deceleration, therefore higher forces on the protection. Unfortunately, my analysis will involve physical modeling.
When is the "moment of the catch"? The freefalling climber reaches terminal velocity right before the rope goes taut, then decelerates until he stops moving downward, and then bounces for a short period.
It may be a natural reaction to try to do this, but I'll bet it is a learned behavior to do it correctly (i.e. without yarding too soon and pulling the climber off his sketchy stance or not having him effectively locked off at the "moment of the catch").