Everyone knows the NFL could reduce injuries even more, but not at the cost of eyeballs. In a purely capitalistic view, players are much more expendable/replaceable than viewers. As a side effect, players will have to accept the risk of being injured for less money than they are now. While a couple of high profile NFL players have retired due to CTE concerns, in general there are many humans willing to make that sacrifice for even a fraction of what players are paid today.
You do that, and you take the wind out of the sails of a sport quickly. You probably have a better chance of success playing fantasy football (you know, gambling) than you would getting rich as a football player.
The adpocalypse is happening right now. We've been warning of it for years. Brands are figuring out their campaigns on "traditional TV" don't return nearly as much as targeted campaigns on online video on a per-dollar basis. The bloodbath is just beginning.
It's just not right to encourage people to do that, and I think a lot of fans are choosing to watch something else.
Edit: Also, basketball has better economics and a more international fan base, so it's probably safe. Baseball is probably fucked too, at least in the current incarnation of MLB. But the NFL is definitely fucked.
Has the popularity of boxing been impacted by this issue?
Also, if the funnel of advertising (and thus TV) money goes away, the visibility of the sport will drop, and visibility reinforces popularity.
If the salary at the highest levels crashed dramatically, the pool of players at every level would shrink accordingly. We would probably see an effect similar to what happened to boxing: the best of the best would still be very good, but the rank-and-file that make up the rest of the sport would be so terrible that most people would lose interest and stop watching. I suspect that fan interest would hold through some level of decrease in overall skill level, but that there is some point where people will just stop watching because the quality of play is so bad (and because of the constantly growing evidence regarding the long-term health implications, which, going back to the boxing example, was another piece of what knocked boxing off its cultural pedestal).