The main issue is that the shelf life of an NFL player is 4 years, so the union is very susceptible to members breaking ranks, and therefore it's a very weak union.
It's a real vicious cycle because the union needs to be strong since their members are putting themselves in harm's way. But since they're putting themselves in harm's way (and their shelf life is very short) the turnover rate of the union members is so high which makes the union very weak.