I'm all for contracts being binding.
However, I think things are a bit different in the NFL. I don't think contracts are guaranteed (which is why the big deal with the signing bonus), which means the team can axe them at any time, and they don't have to pay the contract.
However, I believe the signing bonus aspect of the contract is guaranteed. According to this analysis over half of the salary earned by NFL players is now guaranteed. This number compared to 20% in 1993.
So it seems to be changing. As far as I can tell, the other leagues have guaranteed contracts, where releasing someone merely puts them on waivers, where another team can pick up their contract....but the original team still has to pay it until then.