Increase the playoff pool from twelve teams to sixteen. The controversy this year swirled around divisional winners hosting teams with better records than their own in the wildcard round, but more unsatisfying than the Saints (11-5) having to play in Seattle (7-9) or Kansas City (10-6) getting to host the Ravens (12-4), was the Giants and Bucs (both 10-6) being shut out altogether.
Since the league found the sweet spot with 32 teams beginning in 2002, the regular season win percentage for hosts is 57%. In wildcard games over the same period of time, it's just 53%.
This suggests that strong teams with good records that don't come out on top of their divisions are generally still competitive in the playoffs. This season, three of those potential Superbowl contenders--the Giants, Bucs (okay, a stretch), and Chargers (the Raiders being the other AFC entry if the proposed change were in effect this year)--didn't get in, while the unimpressive Chiefs and Seahawks did. To keep the host-and-be-hosted division rivalries relevant, though, division winners should still be granted a guaranteed berth and minimum #4 seeding. The baby gets split, and everybody is happy!
Well, not quite everybody. The biggest losers (although the teams' owners cash in on this 'loss') in this scheme are the #1 and #2 seeds, who forego first-round byes and are thus required to win four consecutive games instead of three in the postseason to be champions. But NFL brackets are more intelligently malleable than, say, the NCAA basketball tournament brackets are, so the top seeds still get the softest matchups--usually no more than nine wins--at home in the wildcard round. And the #2 seed is still guaranteed homefield until the conference championship, while the #1 seed still only gets knocked out if they lose on their own turf.
Parenthetically, it's really incorrect to describe the NFL postseason as operating under a single elimination bracket system at all, since the highest seed is always pared up against the lowest seed, etc, in each round, irrespective of the graphical bracketing imagery regularly used in (and then often necessarily revised) proceeding rounds. Indeed, this year the initial postseason brackets were 'incorrect' in both conferences (see right), due to only one of four division winners advancing to the divisional round.
This season, instead of enjoying first round byes, New England would've hosted Oakland, Pittsburgh would've hosted San Diego, Atlanta would've hosted Tampa Bay, and Chicago would've hosted New York. The only upset that would've seemed genuinely 'scandalous' in those four games would have been a Raider upset in Foxboro, but that of course raises the question of why a team with the best record in the NFL unable to beat a .500 team it is hosting when it counts should be accorded a freebie win to begin with anyway.