The bottom line is that it's useful in a couple instances.
One is if you're looking at a guy who averages like 20-30 minutes and want to speculate what kind of stats he could put up more minutes and a more pronounced role. Boston tends to have a pretty balanced roster. We were overloaded with mediocre big men. I don't think it was accurate to suggest Jared Sullinger was significantly better than Kelly Olynyk just because Sullinger averaged 13 points and 8 rebounds while Olynyk was averaging 10 points and 4 rebounds. If Sully was averaging 27 minutes while Olynyk averaged 20 minutes, it's fair to even out both of their minutes to make a comparison. 36 minutes is the standardized number available to us. So if you average them both out to 36, you'd see those guys were basically dead even statistically.
The other is to temper enthusiasm about a player putting up huge stats with huge minutes. Jimmy Butler lead the entire league in minutes during his break-out. Some people here had the audacity to call him a Superstar and pointed to his big stats in comparison to guys like Crowder and Bradley as proof. Consider the fact he had more minutes than any player in the league that year. More minutes = more stats. The same issue was present when a guy like Rondo averaged 43 minutes in the playoffs. 43 minutes is obscene. It shouldn't be a surprise that he put up 25% less stats when getting 25% less minutes. If you looked at Rondo's per-minute production during that playoff run, it was basically the same as any other game.
You add in the fact that it was developed at a time when players used to all play 36 minutes if they were a star or good starter and it makes it even more confusing (although everyone here is claiming they would NEVER do that).
I don't think the number 36 matters. I think that's a weird thing to focus on. It's just a standardized minute number. It would serve the exact same purpose if I said, "Rajon Rondo's stats were inflated because he played 43 minutes per game... average out those minutes to 20, and it's roughly the same stats he put up per 20 minutes any other season". It would have the exact same purpose if I said, "Average both Sullinger and Olynyk's minutes to 20 per game, and they put up nearly identical stats". It would serve the exact same purpose if I said, "Average Butler and Crowder's minutes down to 20, their production isn't THAT much different"...
Sites like basketball-reference just have per-36 easily available. They also have Per 100 possessions ... so we could use that instead to compare players and it would serve roughly the same purpose.
Start a petition to change Per-36 to Per-25 or something if it makes you feel better. There were only about 10 guys in the league who actually averaged around 36 minutes last season: Harden, Lowry, Butler, Caldwell-Pope, Hayward, Wall, Middleton, Derozan, Durant, Marcus Morris and Lillard.
The idea is... if we took a guy who is averaging 25 and boosted his minutes to 36, would he put up comparable stats?
Alternatively, the idea is...
14.5 points, 3.7 rebounds, 1.8 assists and 1.4 steals
vs
14.9 points, 3.8 rebounds, 1.4 assists, 1.1 steals
The top is what Kentavious Caldwell-Pope put up last season in 36.7 minutes per game.
The bottom is what Avery Bradley put up in 2014 in 30.9 minutes per game. Would Avery had exceeded Pope's stats with an extra 6 minutes per game? Sure. Would Pope have put up less stats if he hadn't averaged the 3rd highest minutes in the league? Definitely.
Now look at this:
15.2 points, 3.7 assists, 2.4 rebounds, 1 steal.
That's what Isaiah Thomas put up in 25.7 minutes per game on the Suns. That's a full 11 minutes less what Caldwell-Pope got last year. Shouldn't we consider minutes when looking at these stat lines? Wouldn't it stand to reason that Isaiah Thomas would put up better stats than that with more than 25.7 minutes? Yup.