This is Coach Phil Tran, championship-winning high school football coach and award-winning strength coach.
I do not assign push-ups for dropped balls.
Push-ups improve your strength, not your pass-catching skills. No amount of push-ups alone will make a player catch better.
A player who drops a ball in practice needs more practice catching footballs. I will identify why the player dropped the football and work with the player one-on-one during some down time in practice or after practice to improve catching skills.
It makes so much more sense, but for the fact that football coaches historically have been conditioned to think otherwise. That is to believe that fear of physical punishment will force players to perform better.
Perhaps it is not fear that players need, but additional instruction to improve skills and boost confidence. This applies to any skill performed in any sport.
Additionally, push-ups are a healthy, life-long activity. They should be performed to improve health, physique, and strength. They should not be associated with punishment and negative experiences.
Your players need instruction and confidence, not fear.
This Phil Tran saying so long. Go forth and be great.