Average FG% per year in the first few seasons in the BAA/NBA:
1946-47: 27.9%
1947-48: 28.4%
1948-49: 32.7%
1949-50: 34.0%
1950-51: 35.7%
1951-52: 36.7%
1952-53: 37.0%
1953-54: 37.2%
1954-55: 38.5%
1955-56: 38.7%
Any number of theories: talent pool (there is some evidence to suggest this as FT shooting increased from 64.1% to 74.5% during the same stretch), lack of a jump shot so hands in the face had more impact, more physical, poorly run plays, lack of shot clock caused less of a rhythm, even a notion that players shot from greater distances with footage from the '30s showing some players lobbing it up casually from back court before there was a mid court rule because an offense used up the entire court. But when looking over the stats for korfball, another idea came to me. Korfball is an early 20th century basketball derivative. It is like a faster paced and slightly more entertaining netball with some additional intrigue including significant play area behind the basket, fade away jumpers, layups, and mixed genders (so you can meet some girls and some of them look pretty good to me). It was my first time looking up korfball stats. I expected to see 10 columns of stats but I think I saw something like 3, with one appearing to show goals. There were no shot attempts, no shooting percentages. This is pretty much like how stats were kept in basketball before the NBA: they didn't care about shooting percentages, how many goals players and teams got was all that mattered. The efficiencies in how the sports were played were largely immaterial.
Could the use of stats have changed the game? 1947-48 was probably the first time any of them had seen their shooting percentages. A 10% difference in field goal shooting to us is huge, but an eye test has to be fine tuned to 1 more miss or hit every 10. Worse if you're looking at efficiencies of 5%, which requires us to detect which players are scoring 1 shot more or less in every 20 attempts. A general perception could easily be wrong and led to the wrong filtering of talent. Better shooters may have been overlooked because biases of prejudices took over so percentages may have resulted in a slow, but gradual improvement (and also explained the increase in free throw shooting).
It is also possible the game ball may have been a factor. Molded balls were invented in 1942 but it seems (unless this source is incorrect) they weren't officially adopted until the 1949-50 season. So stitching may have affected shooting or affected dribbling which in turn affected shooting.