i just read the small print on becoming a buzzerbeater supporter, and it said a requirement is to weigh in on this debate, so here goes:
i think of solutions as a spectrum, in this case, from status quo to ranges of changes.
-- if one thinks of training as "adding points per game", then (team) FT training is i would guess one of the most effective training practices a manager can use -- up to a point (marginal utility and all that). and that point is reached more quickly, probably, than with other skills (most managers would agree that average or respectable FT produces acceptable results).
-- the irritant is the odd player who just can not hit a FT, the career 0-1000 player. the simplest solution is to devote one week of training, get that atrocious up to pitiful, which usually means to somewhere between 33 and 50 per cent. little time, big returns. the principle of single-position training is useful for those who object to using team training to improve but one player.
-- if this is unacceptable, because nobody misses all free throws, then i would suggest more or less eliminating "atrocious" as a beginning skill as a 18 or 19 year old player -- in real life, it is safe to say, few players are atrocious, but many are pitiful or inept. to balance this, perhaps the speed of ft improvement as a result of training could be slowed slightly.
-- if the game developers are pursuing "realism", then i would have free throws influenced by other factors, including JS, but also experience, stamina, and game shape. for laughs, there could be an unknown cap on ft ability -- i could practice fts till the previously mentioned frogs had figured out how to use their wings, but i would never be a ray allen or dirk nowitzki -- making it in this way similar to stamina or more elusively a player's "physicality".
if forced to advocate for one of these positions, i would suggest eliminating "atrocious" as a ft ability.