I just can't imagine what it feels like to think about giving up $3 mill a year. I am guessing part of what happens is that other people, including agent, family, friends get the player's ear and suggest they should take as much money as they can get.
One other thing I will say, and take it for what it's worth, but some folks who have made a lot of money in sports have gone on to blow a lot of it through bad investments, scams, gambling et cetera (Curt Schilling). Some have dreams of acquiring shares in sports franchises. Crazy as it seems, even these huge sums of money are not necessarily immune from being spent or lost.