“So it seems (from my limited data) that - given enough time - this thing will eventually blow over.”
In cases like this, there’s a phenomenon I’ll call The Tipping Point. The NFL has a number of potentially fatal issues; fatal to the NFL. One is the high number of brain injuries which will, even without the present political issue, potentially end the league. Lawsuits and a dearth of talent coming up from high schools and colleges will, over time take its toll. The NFL has an exemption from the anti-trust laws. This was obtained due to a tainted bit of politics. Now some members of Congress have indicated a desire to revisit this exemption. No telling what the impact of that would be, but whatever it is it will be more than the NFL has had to deal with before this political controversy.
Another factor is that the games have become too long, lasting multiple hours with huge swaths of time for commercials and timeouts, etc. The viewing public is developing a lower tolerance for being bored. Cable cutting and culture changes are already reaping a fairly high percentage of the viewing populace. Combine all of these things with the progressively bad press from hiring thugs who beat up women and do stupid stuff and it is likely that in five years, or ten tops, the NFL will either be dead or nearly so.
What btw, would replace the NFL or football in the future?