Here's my theory: There used to be bigger differences in talent between teams. So teams that had byes were usually quite a bit better than teams that didn't. And when you added in the fact that they had extra rest coming into the game, they would often just roll over the opponent.
Nowadays, with the talent so evenly distributed, more games are toss-ups. Maybe also the game has become more complex in terms of timing, so it is diifficult for a team to be in rhythm after a week off. And homefield advantage seems to be fading in recent years, in the regular season as well as the playoffs. It might be that coaches figured out why they were losing so many road games and have made adjustments in preparation to minimize that factor and maybe even to feed off the energy of the home team's crowd.