While listening to the Saints getting royally screwed out of a game against the Atlanta Falcons in the Falcons' new stadium(C-O-N-spiracy theory being floated around at the time of this writing(Dec. 8th)) is that the NFL wanted the rematch two weeks later on Christmas Eve to mean something because a Saints win would have all but eliminated the defending NFC champions from playoff contention by then), the same two things that seem to plague the Thursday night games reared its head:
1) One team getting too many players injured during the game
2) The game just not being good to begin with
And that's mainly because 90% of the time, the two teams have only two days to prepare for the game. In fact, the Saints got shafted by the NFL's flex scheduling in that the team's game Dec. 3rd in the Superdome against the Carolina Panthers was moved from a 12pm kickoff to a 3:25pm start time because both teams are playing for 1st place in the NFC South division. And it wasn't the first time that happened(in 2014, the Saints played a Sunday night game vs. the Green Bay Packers before playing a Thursday night game against Carolina in Charlotte).
The NFL is not going end the Thursday night games anytime soon as long as they're getting millions of dollars from both the legacy TV networks(CBS & NBC in this case) and the internet streaming sites(Amazon Prime in this case; last year, the NFL had a deal with Twitter to stream Thursday night games online. While it was a one year deal, the NFL probably would have found a way out of a long term deal with Twitter losing users and having no user growth in the last year between the draconian rule changes, unjust bannings of certain people, and new similar platforms like Gab & MInds popping up).
So here's how the league can improve player safety and make the games more watchable:
1) Expand the bye weeks from Week 2 through Week 15. That way every team plays Week 1, Thanksgiving week, Week 16, & Week 17. And as LiveJournal user Freezer suggested, teams getting the bye week play the Thursday night game the following week. WWL Radio host Kristian Garic(also Saints radio sideline reporter) has suggested giving teams two bye weeks(which the NFL did try during the 1993 season).
2) Work out a deal with NBC to air a Thursday night doubleheader(like the Monday night doubleheader on ESPN) or even a Friday night game on opening weekend and have one team from each game play the Week 2 Thursday night game like the NFL already does with the Thanksgiving Day games(two of the teams playing on Thanksgiving Day play the following Thursday).
3) Expand the rosters to 60 players(and letting them all dress out for the game as opposed to having 46 for the game) and expand practice squads from 10 players.
Another way the league can improve player safety: Add the targeting penalty from the NCAA where any helmet-to-helmet hit gets a player ejected from the game(not just for hits on the quarterback or a defenseless wide receiver).
Also, there's no real difference between running into the kicker and roughing the kicker, so just do like they did with the face mask penalty(used to have a 5 yard penalty for inadvertantly grabbing the face mask, but the league got rid of it and just made all penalties for grabbing the face mask a 15 yard penalty) and make running into the kicker in the act of kicking the ball a 15 yard penalty regardless.
-Note: This was written before news came out about a former Falcons player being one of the referees for the Saints-Falcons game.-