I believe the article contains the answer to the question regarding why NFL players are more socially active: “The first part of that is pretty simple. Players have short career shelf lives….”
NFL teams are not a democracy. They sign players and, as long as those players abide by the rules and continue to perform at a given level, they continue to draw a paycheck. In Mr. K’s case, he’s sitting already because his performance on the field is significantly diminished from the heady days that caused the club to trade Alex Smith to KC.
NFL players do indeed have a short lifespan, playing-wise. I would imagine most players weigh the pros and cons and decide they can wait until the retire (late 20s ~ early 30s) before exercising that aspect of their hard-won freedoms.