Free throw percentages in the NBA over the past 50 years have remained remarkably constant, hovering at around 75 percent. Since most other tangible facets of the game have improved in that time span, it is puzzling that there has not been much change in free throw percentages.
My explanation of this phenomenon is that there has not been much selection pressure towards better free throw shooters. Most NBA teams emphasize size and athleticism, arguing that if you are outmatched in those areas you will be so dominated in other areas that free throw shooting will be irrelevant. Moreover, free throws are seen as something that you can teach, but you can't teach height, and you can't teach tomahawk dunks.
Finally, even if NBA teams do have a preference for slightly better free throw shooters, that effect will be counteracted by concurrent preference for slightly bigger players. Big men will always have a tougher time shooting free throws. This is partly due to simple biomechanics--image trying to throw a tennis ball into the hoop and you understand Shaquille O'Neal's daily struggle. It is also partly due to reduced incentives for those 7 feet and over. Even if Andrew Bynum cannot shoot free throws well, he will still have a job somewhere in the NBA because of his abnormal size, whereas a 6'2" player would not be able to survive with a 60% average.
Assuming the inflation-adjusted wage stays relatively constant or increases, and as the global talent pool increases, this model predicts that either players will continue to get taller and stronger or average free throw shooting will improve. The 2006-2007 NBA average height was 6'6.9" and the average free throw percentage was 75.2%. I am willing to bet that, assuming the inflation-adjusted wage of an NBA player stays the same and the league has not expanded drastically, one or both of those measures will have increased by 2026.
Seth Roberts reports that Cal Tech's had one of the top basketball teams in the nation during the 1950s! As Seth notes, in the 1950s you would look at that and think "well that's just how it should be," but now it looks so weird.