It's a myth that FT shooting averages have been declining in the NBA. In fact, there are more excellent FT shooters than ever.
I doubt it's about lack of discipline and practice, shooting ft is very mental. Lots of NBA players who are average FTers on game situations can shoot and make lots of consecutive free-throws in practice. It's not easy to correct FT mechanics, because the angle and speed of release to each player is unique. Also, your athleticism is conditioned to make the regular shooting (the "muscle memory" thing), which makes harder to correct the FT mechanics. This is even more serious with big guys, who are not used to use their legs to shoot. This is also the reason why is more difficult to improve FT% at a later age, you've already acquired bad muscular habits. Bird used to shot 200 FT every morning before going to school. Had he started doing that only in college, he'd never be as good as he was. But essentially, is a mental thing for the most part.
To some extent, there's also a genetic factor. It's more difficult to model your shooting mechanics when you have long arms and big hands, one of the reasons why many post players (or Rondo) struggle making FTs.
But yeah, some teams have improved substantially their collective FT% after hiring some coaches who are specialists on the issue. I don't know if the C's have a FT coach, I don't think so.