They are very different sports. NFL players get injured because the sport can cause injuries in almost every play and situation. Taking games off or lowering their number of plays per game does not really make it less likely that someone will get injured. It just reduces the number of opportunities to suffer an injury.
NBA players don't face nearly as much contact, obviously, though guys who play 40 minutes actually play 40 active minutes. In the NFL you have offense, defense, special teams, more rotations and lots of inactive time. The question is can more rest actually prevent injuries. In either sport (but it seems more likely in the NBA).
Obviously players in both leagues like load management and in the NFL's case do not like the new scheduling trends. But they like the money. The players would certainly not want to take a pay cut for a reduced schedule anymore than the owners really want to give up revenue.
Injuries just happen. Look at Rhys and Christian Pache. Neither load management nor less contact would have helped them.
