I once had dinner with Rick Barry. He told me he'd been working with Shaq underhanded in the off season and he was making near 80%. He asked him if he was gonna do it and Shaq told him he just couldn't shoot underhanded. Would ruin his image. Barry told him he'd destroy Kareem's all time scoring record and shaqsaid he didn't care, Shaq don't shoot underhanded
The "granny" shot would improve just about any players FT percentage by 10-15% that has difficulty. Perhaps more than that depending on what they are shooting now. You can control the direction of the ball much better and it is a soft shot. Any shot that is soft and online has a fantastic chance of going in as long as it gets there. If you don't believe it try it if you have a chance.
The comment by Shaq just goes to show that looking "cool" or "macho" means more than winning games for men. Although I also don't see women trying it either.
I guess it is kind of like dunks. How many times have you seen a player go for a monster uncontested dunk in a close game where the choice was to dunk or just drop in, and the result with the dunk is the ball hits the back iron and caroms halfway to midcourt. I know it has happened to us a few times over the years.