Making the second round of division games the last three games of the season would be a great idea. Because you know those teams are probably going to go balls-to-the-wall to beat their rivals and hope to get that division title.
And I'm not arguing that how the Jets got in seems kind of cheap. I'm not arguing that at all. What I'm saying is that the NFL is kind of handcuffed on what to do about it, don't you think? I mean, they can't step in and tell the Colts that Peyton Manning HAS to play a certain amount of snaps just so another team in the league has an equal shot as the team they're playing.
As for the proof supporting NOT resting your players, people can (and will) argue about that until the cows come home. I, personally, feel it's a much better bet to go in the playoffs on a roll and a winning streak, than resting your players and taking a few losses. But I'm not Jim Caldwell or Sean Payton, so I don't really have a say in the matter. They're the head coach, and I'm not, so I'm going to assume they have a better handle on their team than I do.
Does it suck that this particular scenario happened? Yes, it certainly does. Is there a lot (outside of your suggested divisional games as the last three games idea) of solutions to the problem? No, not really.