They should expand the playoffs first before considering such a change to the regular season. I like the regular season format as-is, where you get to play everyone at all stadiums at least 2 times in an 8-year period.
The playoffs have needed expanding for quite some time. It's been needed since 2002, with the move to 8 divisions. At that time, the NFL decided to sacrifice a wild-card team in each conference in favor of another division winner, rather than expanding to at least 14 and keeping the number of wild card teams the same (or possibly more).
Between 2003 and 2015, numerous 10-win teams missed the playoffs despite fielding decent squads that year. In one case, an 11-5 Patriots team was cut off, but the team has made 10 straight playoff appearances since (an NFL record). For some other teams, missing at 10-6 was such a disappointment that the teams had long stretches of consecutive losing seasons afterward. Such cases include the 2007 Browns (who became the second 0-16 team a decade later, but now seem to be on the right track despite a 1-2 start this year), the 2012 Bears (who finally returned to the playoffs last year), and the 2015 Jets. Thankfully every 10-win or more team has made it in the last three years, the first multi-season streak of this happening since 1992-2002.
Also, since the last NFL playoff expansion in 1990, each of the other two major outdoor sports leagues in the US (MLB and MLS, the latter only established in 1996) has expanded their playoffs twice, and with three teams seemingly deserving of Wild Card berths in the AL this year, another playoff expansion in MLB may not be far off.
Another reason is that for several years no team that had to play in the first round has played in the Super Bowl. Expanding the playoffs to 16 teams negates that advantage.
This brings me here:
The NFL is now permitting local markets to air another NFL game opposite a team's home game, though this won't always happen (some teams are enforcing the old rule this week for instance).
The next step to evolve Sunday afternoon coverage is introducing a "reverse mirror", in which one of CBS or Fox's regional games in each market would also be carried on CBS Sports Network or Fox Sports 1.
The reverse mirror can be used to primarily distribute the top 2 games in a timeslot outside of markets where they are airing on CBS or Fox. Sometimes it can also be used to air another locally popular team kept off of the local CBS or Fox affiliate by the secondary market rules in a given week. Such cases where this might happen include Harrisburg, PA, where Steelers games airing at the same time as a Ravens road game can air on CBSSN (if the game is not on Fox instead). Or in Ohio, where the reverse mirror can distribute simultaneous Bengals and Browns games to most of the state. Or even in Florida, to expand in-state distribution of simultaneous Dolphins and Jaguars games.
In my proposal to expand the playoffs to 16 teams, the reverse mirror would also be utilized in the 1 PM slot on both Saturday and Sunday of the first round, with one slot going to CBS/CBSSN and the other going to Fox/FS1, alternating each year. This is a creative way to avoid playing playoff games on days other than Saturday or Sunday.
Of course this wouldn't happen until 2023 at the earliest.
And to make things more interesting after expanding to 16 playoff teams - division winners are no longer guaranteed a top 4 seed. This means you could win your division and still only get a 7 or 8 seed because you won a weak division. So more teams would be playing for seeding in the playoffs in the final weeks.