History does not project well for the turnaround that we've hoped for (and definitely haven't seen so far).
It's quite possible that last year was his free throw ceiling. He shot 29% in college and is shooting 17% this year. At the moment, he's a 35% career shooter. And no one in NBA history has come close to that level of ineptitude. See here: Really Bad Free Throw Shooters
We all sort of expect improvement over time. But Dwight Howard (a 58% shooter) had his best season as a rookie and his worst have been his last three seasons. Similarly, Shaq -- bad, but only the 10th worst of all time -- shot only about 48% after his first two seasons, actually dropping about five points.
Ben Wallace (41% for his career, an all-time low) was as bad as Andre for seasons one and two. But Ben never cracked 50% for an entire season and remained consistently terrible for his entire career.) I guess averaging 42-43% over the next fifteen years was an "improvement", but nothing to get too excited about.
Chris Dudley was awful. He finished at 46%. His first season was his best at the free-throw line, but his next three were collectively his worst. For the next 10 years, he moved between 44% and 53%. Really no improvement here.
Adonal Foyle was 42% after five years. He did average close to 60% for the rest of his career (including a bizarre 67% in a season in which he took the largest number of free throws). So, this is one precedent for an awful shooter significantly raising his performance.
Greg Kite was 43% after 4 seasons and managed to shoot 50-58% during his last four full seasons. So that offers a little hope, too.
Andre's peer -- DeAndre Jordan -- was a 38% shooter after two seasons. Since, he's been about 44%.
Dan Gadzuric was *above* his career average in two of his first three seasons. So not much happiness there.
Thus, in the history of the NBA, I'm only finding Adonal Foyle, DeAndre Jordan, and Greg Kite as precedents for awful free throw shooters who even managed to add 5-10 points to their averages after a couple of seasons. The others profiled essentially got no better. Howard and Shaq got worse (and both of them started twenty points ahead of Andre).
You gotta think that all of these players (or at least most) were professionals, who cared and wanted to improve. Roughly a third got a little better, a third stayed in the same range, and a third got worse.
Doing me a little estimating based on past performance, Andre wouldn't look likely to even catch up with all-time worst Big Ben. And there seems to be some reason to fear that we've already seen his best free-throw shooting days.
How big of an Achilles heel is this? Andre is compared to Howard a lot, but Howard has hit at a 60% higher rate than Andre. Since his first season, opponents have put Howard on the line 10 times per game. At what point do opposing teams start making Drummond shoot 15 or even 20? Twenty free throws is 10 possessions and hitting six or seven a night would regularly cost the Pistons 4 or 5 points. How many games a year are decided by two, three, or four points? (Of course, we are hoping that Andre becomes Howard on defense and that could happen. On the other hand, the current gap between the two in that regard is also pretty huge.)
Bottom line question: if Andre Drummond is a 35% free throw shooter for his career -- and this results from 10-12 shots per night -- can he legitimately develop into a franchise cornerstone? That's a lot of wasted possessions every night.