I went back a little further (through 2003), just to see if I could find a team with a losing record who would have made it. I did not. From 2003-2009, there were another three instances of 8-8. Everybody else was 9-7, 10-6, or in one case, 11-5 (2008 Patriots). Altogether, 17 years, 34 teams, eight of which were 8-8. Everybody else had a winning record, ranging between 8-7-1 and 11-5 (with by far the most common record being 9-7). Conclusion? There will be a few exceptions, but in most cases, the change will add another team to the mix that is SLIGHTLY better than average, while taking the bye away from the 2nd best team in each conference. Meh... I don't think the former is worth it, at the expense of the latter.
In other words, which adds more meaningful drama to the NFL regular season and playoffs? Playing games in Weeks 16/17 (or 18?) that decide who gets the #2 seed and a bye (which significantly increases their chances of making the SB)? Or playing those same games in Weeks 16/17 to see who gets in with the 7-seed at 9-7 (and has almost zero chance of making the SB)? You can argue one way or the other, but in the overall scheme of winning a title, one is much more impactful. More isn't always better, and in this case, adding more teams looks a lot more like the NBA, where the latter half of the regular season and first round of the playoffs are a snooze-fest, than March Madness, where parity runs rampant and anybody can seemingly make a run.
All of that said, would this change ruin the NFL playoffs? I doubt it. I'm a traditionalist, and don't see the benefit in adding teams. But, the first couple of weeks of the NFL playoffs are (and will likely remain as) some of my favorite sports weekends of the year. I'm a college hoops nut, and they're better than March Madness. I'm a golf nut, and they're better than any major. I just think four games during wild card weekend is plenty. Six feels like watering it down.