Mind you, this is only what I once read (back when I cared about the sport I played at U-M): Hall-of-Fame hitting machine ROD CAREW regularly consulted a hypnotist. How much that had to do with a .328 lifetime average or seven(7) batting titles is debatable, but it obviously didn't HURT his prowess.
I've never played organized basketball, but I have to agree with coach B: FT shooting success/failure is at least 50% mental, for the AVERAGE player.
As an addendum to your, point, 'Shoes, I also played (sandlot, not college) tennis for decades, and knew many, many people (myself included) who hit groundstrokes very well----DURING WARMUP. Once the match started, the net was a MAGNET for their shots.
Do you think it could be (as with bad FT shooting) a type of "mental block" that in a GAME (or match), misses/mistakes COUNT FOR SOMETHING, and something bad, whereas in practice/warmup/driving range, you think what the hell, just hit or shoot the next ball?