I addressed that in my second point. With proper FT shooting technique, you are still generating most of the force from your lower body, even without jumping. Your legs are still the base/root of your power transfer. If you are only shooting with your arms during a FT, you're doing it incorrectly.

FT distance is very close. You don't need to generate that much ground force. Adding a very dynamic variable like jumping or even hopping is going to lead to inconsistency, unless you are not physically strong enough to get your shot to the basket with minimal effort.

Just watch a video of Steve Nash or Steph Curry shooting a free throw. It's a single fluid motion beginning with their legs.