Wild Cards and Meaningless Games in the NFL

It seems every season there is a discussion about teams resting their starters for meaningless/nearly meaningless games at the end of the NFL season. These discussions get a little confusing because there are three different questions associated with the problem. This season the questions have come up with the Colts-Jets game last week and the Bengals-Jets game this week. Since most writers at least relate to the first two issues, I will just link to a number of examples to begin with (see here,
here,
here,
here, here and here)

1. Is it optimal for the team to rest starters? The optimal choice in this question differs between the Bengals and the Colts. When the Colts played the Jets, they still had one regular season game and were locked into a bye. A case could be made that they took their foot off the gas too soon. In the Bengals case, however, it is their last game and they will not be getting a bye, so they will have to play next week as well. Not only that, but their last playoff trip was ended when their quarterback got injured on the first series of their first playoff game. For that reason, I think they will be a little worried about injuries. I think I would be inclined to not go all out in the last game.
   
2. Is it moral for the teams to not try/go half speed in games that don't matter? Is it ok to do so unless the other team is going to be in the playoffs? I will not discuss the first question, but I will point out a problem with answering in the affirmative to the second. Let us say that the 4 and 5 seeds are locked in place, but that the 4 seed is playing a contender for the last playoff spot and the 5 seed is playing non-contender. If there is an advantage to resting players (see question 1) then the 5-seed would have an advantage over the 4-seed. That result does not seem fair to me.
   
3. Is there a way to design a playoff system that does not lead to teams resting players for key games for other teams? Jerome Bettis suggests that the NFL fix this problem but does not suggest any solutions. One reason he does not suggest a solution (and for that matter why the NFL has fixed the problem yet) is that there are no easy solutions to this problem. Pro-football Reference suggests three proposals that would help in some circumstances. Proposal 1 would eliminate the automatic home game for division winners, meaning that relatively poor teams that have clinched the division would still have an incentive to win to get a better seed. Proposal 2 at the same link would have a flexible number of playoff teams, meaning a 2-seed would lose its bye unless it was at least three games ahead of the 7-seed. The third proposal would be to have flex games for the last two games of an 18-game schedule. These flex games would be chosen so that playoff contenders played other playoff contenders. There are a couple of problems with these solutions. Proposals 2 and 3 are pretty revolutionary. Proposals 1 and 2 would not have fixed the Colts' and Bengals' problems this year, not that fixing this particular problem was the only idea behind the proposals. The only way to completely fix this problem would be to have no wild card teams and guarantee that teams only play intra-divisional games the last two weeks of the season. So unless you are willing to suggest that or something truly unusual like the above, it is simply a problem you will have to live with.