In my opinion, I wouldn't mind if the NFL extended the season, but only if the extra games involved are inter-conference match-ups (NFC vs AFC). Think about this: An NFL team only plays 13 different opponents per season (Considering that same team plays their division rivals twice). Out of those 13 teams, 9 of them are from the team's same conference and only 4 are from the other conference. I could see the league extending the season to possibly 19 games if they use the 4th rule of their scheduling formula for the opposing conference: The current rule: "Each team plays once against the other teams in its conference that finished in the same place in their own divisions as themselves in the previous season, not counting the division they were already scheduled to play: one at home, one on the road (two games)."
The New rule: Each team plays once against the other teams in its conference that finished in the same place in their own divisions as themselves in the previous season, not counting the division they were already scheduled to play: one at home, one on the road (two games) AND once against other teams in its opposing conference that finished in the same place in their own divisions as themselves in the previous season, not counting the division they were already scheduled to play. (three games)
In this case, if that rule went into effect this year, for example, the Lions, who finished in 3rd place in their division, would also be playing the Dolphins, the Browns, and the Texans this year, since they finished in 3rd place in their divisions last year as well, along with the AFC West teams.
At least with this new rule that I made up, the schedule would be more balanced conference-wise, 9 teams in the same conference and 7 (as oppose to 4) in the opposing conference.