Wow, lots of complicated suggestions. I don't know the answer. The base question here seems to be whether there should be a 65 game rule for season awards. Then it got conflated into a question about load management in general (or so it seems).
There are not that many players in the league that are legitimately contenders for MVP. I don't really like the rule as it applies to MVP (or other awards). If a player gets injured and misses 20 games, that should be a factor but I don't like the hard cut off. Play 66 games and you are OK but only 64 and you don't qualify?
I believe that a first place vote is 10 points, second is 7 and so on. Maybe make it that if you play less than 65 games, then your first place vote is only worth 9 points, second only 6 points or something. That way it is still a factor but not all in or all out.
As far as load management, so long as there are back to back games, all teams are going to rest some players. Eliminate back to back games and there would be less of this. Some players need rest along the way or they won't get through the season. I don't see this as a major problem and also no realistic way to change it.
But load management is literally the only reason the rule exists.
Otherwise it makes no more sense than adding minimum criteria for points, assists, or rebounds.
If that is true, then the rule is misguided. Take Jokic for example, he has missed some games purely due to load management but the majority of the games he has missed is due to a legitimate injury. Same with Cunningham, same with SGA. If you get a player like Kawhi Leonard, whose knees are about shot, he may be load managed to a point where he gets below 65 games, but he won't be getting MVP votes. And I don't think this rule will affect how many games that Kawhi plays. They are going to rest him as much as they need to.
Resting a player for purposes of tanking is different than load management. I see tanking as a real issue, I don't see load management as something that can be eliminated.
Another way to approach is to look at stats from a season total standpoint, not average per game. Who scored the most total points. Who got the most total rebounds. If someone was changing the scoring title, they might stay in some games to get more points.