They could have a round of 32 like the NCAA tournament, including every NFL team in a playoff, and the regular season still wouldn't be diminished. This is the best sport on the planet, with a limited number of games. This wouldn't change that.
Even if this is in jest, I liked it. And I have a proposal to make it work. All 32 teams in the NFL post-season tournament, without diminishing the regular season.
SOLVED:
For each conference, consider the 4 divisions with 1st through 4th place finishes
E-W-N-S
1-1-1-1
2-2-2-2
3-3-3-3
4-4-4-4
Week 18 (3s play 4s)
Week 19 (Week 18 Winners play 2s)
Week 20 (Week 19 Winners play 1s)
In this scenario, the 2nd place teams in the division get a 1 week bye and the 1st place finishers get a 2 week bye.
EVERYONE is in. Higher seeds get home field every time.
I hereby allow ROD to patent the NFL post season brackets for this new format. All glory to ROD. In ROD I trust. Amen.