A few things.
First, basketball is NOT the most streaky sport, and it's not even close. Baseball is the most streaky, the most luck-based. This is due to the fact that Baseball's whole scoring system is based on stringing together multiple low chance successes. Further, Basketball is actually the MOST consistent sport of all the major American sports. Records and winning is the LEAST luck-based due to the large number of possessions and the relatively even schedules by all teams.
Second, how much Andre needs to improve his free throw shooting is more complicated than just an arbitrary feeling for what's good enough. Some stats: Detroit averages 1.02 points per possession, Drummond himself shoots 51.7% from the floor, and league average shooting efficiency is about 54% TS. Sending Drummond to the free throw line in general has an expected outcome of .69 points (in intentional foul situations this actually drops to about .5 expected points). So, for Drummond's free throws to be no less valuable than a regular possession, he would need to hit them at roughly 51%. For Drummond's free throws to be at least as good of a shot as a non-fouled shot, he'd need to hit roughly 52%. And here's the bigger one: if Drummond wanted to score at league average efficiency, he'd need to hit 55% of this free throws.
Right now, Drummond is actually a wildly inefficient scorer for a big man. He has only one real scoring skill, which is the dunk. That's a wonderful shot, but exclusive dunkers like Drummond need to shoot a lot better than 51% from the floor (~60%). In lieu of that (much of that is Stan trying to get him to expand his skillset), he simply HAS TO hit more free throws. And in an interesting twist, just shooting 51, 52, or 55% from the line has diminishing returns, because if Drummond hit more of his shots he wouldn't get to the line as much. For Drummond to become the truly dominant player we need him to be to contend, Drummond would need to be an efficient scorer - requiring both an increase to FG% and FT%. A 16% increase to Drummond's FT% should be the bare minimum, and that alone would simply stop making him an intentional foul target rather than actually improving the offense.