In Writing with Hitchcock (2001), Steven DeRosa noted that Hitchcock supervised them through every draft, asking that they tell the story visually. He told Roger Ebert in 1969: Once the screenplay is finished, I'd just as soon not make the film at all.
A drop kick is a type of kick in various codes of football. It involves a player dropping the ball and then kicking it when it bounces off the ground.
In other words, organic toontanics (and pianos too!) do the same thing as inorganic ones. It's not as useful lure, trap or throw (and even toon-up) because drop is the last gag track to do any kind of damage in battles and requires a stun, and to stun you need some kind of damage anyway. Drop is all about finishing a wave of cogs, the grand finale and I don't think you need extra damage for it.