Very debatable how much the removal of hand checking has changed scoring averages. League scoring averages changed drastically at other times before hand checking was ever removed in 2004. Scoring in the 80's and early 90's was much higher than it was in the late 90's and 2000's. Scoring really started to drastically increase long after the hand checking was disallowed.
I'd argue that the single biggest factor that has affected scoring over time is style of play, driven largely by the most successful teams in the league. In this copycat league, most teams try to emulate the style of the teams that win. League scoring average was well over 100ppg from the 70's to early 90's. The pace of play really started to dip in the mid 90's - probably largely due to the success of the Bulls and other champs of the era. The triangle is a very slow-paced, methodical offense. When the Bulls paired that with a dominant defense, and especially as they aged, their scoring dipped into the 90's and the league followed. Everybody thought you had to play a slow-paced, defensive-minded game that valued possessions in order to compete. And it wasn't just the Bulls - mix in the inside out, post oriented offenses of the Hakeem Rockets, the TD-Robinson Spurs, another few years of triangle dominance with Kobe and Shaq, and everybody thought you had to have a post-oriented, slow-paced offense to have a shot at winning. The year hand-checking was disallowed, league scoring only increased 4 ppg from 93ppg to 97ppg, and hovered around or below 100ppg until about 2016. 2016 and 2017 scoring bumped up a bit to 105ppg and 106ppg, and has been over 110 ppg since 2018.
I don't have to say what caused scoring to increase by basically 10ppg from 2015 to 2018. It took the league a few years to fully embrace the Warriors style - and I wouldn't just say it was the Warriors. The Spurs last title was much more of a ball movement, 3-point based attack as well and no doubt had a lot of influence on Kerr's offense. So basically my thesis is that removal of hand checking at best added 4-5 ppg scoring. The success of the Warriors and realization from the league that you had to bomb away to efficiently compete added 10 ppg. And btw, the highest-scoring era the league has seen was the 60's with no 3-point line.
Also, here's 20 minutes of Isiah scoring in the paint in the late 80's / early 90's, largely untouched, to illustrate how stupid it is to say Curry would never score in the paint in that era and would get put on his ass every time he tried.
