If that is really true, then yes, they should be. However, I'm not convinced that it has been "proven." Maybe there is some evidence to support that, but I'm skeptical. It might be better for some people, but not everyone, so perhaps players that struggle shooting free throws the standard way should try out underhanded free throws.
No, it is unnecessary to reteach NBA players on how to shoot baskets from the line. Professional basketball players already know how to shoot using an underhanded style. As professionals, they know what shooting method works best for them whether the throwing styles that they use are underhanded or overhanded ones.
NBA players should not be retaught how to shoot from the line. Even though "granny-style" shooting is physically proven to be the best way, each NBA player has their own unique body shape and athleticism. Each player should be able to choose and decide for themselves what shooting style is most comfortable and compatible with their approach to the game and their physique. There is no "one size fits all" formula.
None of this "granny-style" basketball net throwing. It looks comical, if not unprofessional. Basketball players do not need to be re-trained in how to throw a basketball from the line. Players must practice on a weekly basis, and strive to improve their performance in every game. They must play as a team and support each other. Players should have a good connection with their coach, and be prepared for every game. A free throw or two is acceptable, after a couple of hours of vigorous play, but it isn't the type of play to be encouraged.