Maybe what the league needs to do is formally designate injury vs. rest. Not sure exactly how it would work but perhaps an injury is a minimum of 3 games or 5 games or something. So if you deem a player "injured" that player must be out for at least 3 games or 5 games.
"Rest" games could be one game at a time but there is a maximum number of rest games that a player can miss and still qualify for awards (pick a number, 5?, 8? 10?). Extraordinary Circumstance missed games would not count against the "rest" games (babies, family emergencies, etc).
Then leave it to the voters to decide based on injury games. If a player missed X games due to actual injury, the voters can consider this.
I don't think that's a bad idea actually. there'd obviously be some gamesmanship over how team's qualify Injured from Rest but I think that's a good concept to start with. Cap the number of Rest games at say 8-10 for a season to restrict qualifiers for awards and let the Injury/Circumstance days be part of the consideration for the awards.
The league's argument about fans wanting to see the star players actually play - whether in person or on television -- rather than sitting out for rest or fake injury looks a lot more suspect in light of the league's taking away the fans' ability to see those same players on the league's greatest stage (the playoffs) by putting games on streaming services that fans do not subscribe to nor are likely to do so just to see a handful of games and incur yet another unfair cost just for being a fan.
There would be gamesmanship but that is the idea behind the point that if you declare a player "injured", it has to be for a minimum of more than 1 game. Pick a number, 3 games or 5 games. The would separate out fake injuries from the real one. You could still fake an injury, but you would have to keep the player our for say 3 games, not just one game. If it is just one game, it counts as rest.
I am sure there would be issues around the edges of this. Say a player gets a tooth knocked out and legitimately needed to miss one game. Or got a cut or something. But I think this could impact the choice to rest a player. You can still decide to rest a player, but there would be a penalty for it.