It's an older article (2011), but interesting. Players improve on average by 0.7% in ft shooting per year up to age 27, then level off. That is a surprisingly low number considering all the time and practice I assume players put in.
It does make me wonder... why do players spend so much time practicing FTs if it is translating to such little gain? Are the hours of practice every day necessary to maintain their current levels? Or is their expectations of improvement misguided?
I'm surprised that more attention isn't devoted to Karl Malone, Chris Webber, or whoever their coaches were when a team wants to help a notoriously bad ft shooter become better.
http://www.basketballprospectus.com/article.php?articleid=1611