How so? I'm sure the league could have an air tight document drawn up that, once signed by a player, dissolved the league of all culpability in the event of injuries sustained in a practice and/or game. It would basically say that everyone understands the risks involved in playing football and the player assumes all those risks as a condition of entry into the league. The league would show good faith with rules designed to limit injuries, heavy punishments for breaking those rules, and a strong insurance program for players.
There are all kinds of places that make you sign waivers that basically say "participate at your own risk". I don't see why the NFL can't operate in the same manner.
Sorry but no. You want proof? The proof that such a waiver can't exist is that it doesn't exist. If it could, every ticket you ever buy, every contract for car every car purchase, every sales receipt for every item you buy would include it. The law doesn't allow such blanket waivers for obvious public policy reasons.
Go to a baseball game and get hit with a foul ball, and the law says you assumed that risk. However, that risk is statistically minor and you have an enormous ability to minimize (or eliminate) it by your choice of seating.
Enter the NFL and despite whatever you're being paid, your employer can't subject you to unreasonable and preventable risks to your health. Hurt your knee in a single catastrophic hit -- that's part of the game (for now). Sustain even a couple years of direct hits to the head that better gear or monitoring could help mitigate -- well, that might not be part of the game anymore.