First, I totally agree on how money has gotten so out of whack in some professional sports, it has really made me want to just walk away.
That said, I am not sure I would lump Rodgers into the class that you might be implying he is in, since I think he does actually love the game. However, you are right, some players can take the money and run and be set for life. While the "set for life" probably didn't occur as much 50 years ago, I am sure players became less motivated and just played for whatever they could get or walked away.
Today's professional athletes, in the major pay sports are really in a "unique" situation, the money is way more than playing the game is worth, but is the game worth playing, once they have enough money? Rodgers doesn't "need" another $10M/year, but for him it is probably more the status and recognition that comes with the pay. Of course, maybe being able to buy himself another few percentages of Bucks ownership might be motivation too.