um I never said the rest of the minutes in the year don't matter. In fact that is just nonsense as of course they do, it is the accumulation of entire seasons that wears on a player. That includes travel, practice, games, and everything in between. Age is far less important then seasons.
Too much black & white thinking here, IMO.
Age has a huge direct impact on performance, This has declined somewhat over time, due to more advanced fitness, nutrition, training, etc. But still, all of modern technology maybe extends careers by a few years. Almost zero players excel athletically in the NBA past age 35 then and now.
On the other hand, wear & tear is important. This is both cumulative, i.e. my knees are bone-on-bone after 30,000 minutes played, and random -- if you play 1,000 games you have many opportunities for random injuries.
It's impossible to totally separate the two, but the way I see it:
1) The effect of age is very well understood and only slightly changed over the past 50+ years. 40 was old then, and it's still old now. The vast majority of players see a steady decline after age ~30ish, and those that don't decline often are making up for it in other ways (i.e. their body is in decline, but their overall game is not).
2) Minutes played is somewhat a factor, if for no other reason that the random chance of injury. A player who joins the league at 18 vs 22 might have another 250 NBA games in which to get hurt by age 30. They may add to a degenerative condition by a year or two down the road. It's hard to quantify exactly, because it's more of a compounding factor on top of the inevitable aging.
TL;DR; aging is a given, and playing more in your 18-22 years may very well compound it later, but it's very hard to separate the two. How many guys enter the league at 18? Are they already more physically gifted than players that join at 22? Are they more or less injury prone? There's just not a ton of data. You can count teenage NBAers with long careers on one hand, almost.