College football is the sport that is culturally most accepting of ambiguity in its champion. It went more than a century without having so much as a formal national championship game, and even once it got one, the first incarnation of it came from a system that didn't include two of the major conferences. As recently as 2003, most fans nationally recognized college football as having two overall champions.
It is ironic then that it's also the sport most concerned with having a champion worthy of the title. The NFL champion is rightfully whoever wins the Super Bowl, even if that team barely made it above .500 in the regular season. The MLB champion is whoever wins the World Series, even though a 162-game regular season is a far better barometer of team quality than seven-game series are. The college basketball champion is whoever wins the NCAA Tournament, even if that team was a distant third in its own conference and only managed a 7-seed in the bracket.
In college football, there are endless arguments over who is the best or the most deserving team to play for the championship. That really does matter to fans. The postseason format therefore is kept exclusive in no small part to try to remove the possibility of having an unworthy champion.
The sport itself seems to have some antibodies against unworthy champions too.
Partially it's that the cream always rises to the top. In mid-September of this year, there was speculation about BYU causing chaos for the playoff committee after it beat Nebraska and Boise State, but the Cougars finished the month 2-2. In 2007, Kansas nearly rode a horrible schedule to a national title opportunity, but Mizzou beat the Jayhawks at the end to remove that possibility. The 12-0 Iowa team that played for the Big Ten title this year wasn't seen as truly a top team either by fans or advanced stats, and Michigan State took care of that for everyone.
There were a couple of years there in 2001 and 2003 where the a Big 12 division winner got blown out in the conference championship game and still got to play for the championship, but that happened because the people running the BCS had no idea what they were doing with the formula. Plus, neither of those teams managed to actually win the national championship. College football's antibodies defeated those threats.
The old poll system and the BCS sometimes kept teams that would've been deserving of the title "champion" out of the top spot. The 2004 Auburn Tigers come first to mind around these parts, but there are plenty of other around the country who would argue for other teams from other years. For instance, I know that a lot of USC fans believe their 2008 team would've beaten Florida for the national title. The extreme exclusivity of either having one eligible team for the title (the poll system) or two (the BCS) generally kept out undeserving teams.
The College Football Playoff expanded the field of participants in the national championship tournament from two to four. The championship tournament lost some exclusivity, but it did so with a tradeoff. It traded some exclusivity for an added opportunity for testing potential champions.
Let's go back to that Iowa team that finished the regular season 12-0. No one would've accepted that team as champion at that point, but it still had the Big Ten Championship Game left to play. I'm not sure if many people would've accepted a 13-0 Iowa as a rightful champion had it beaten Michigan State either, but the Hawkeyes still would've had two more games left to play.
That 13-0 Iowa team would have had to win contests over undefeated Clemson and the Alabama-Oklahoma winner to come away with the national championship. The hypothetical 15-0 Hawkeyes team would've ended up with three wins over teams that had no more than one loss to anyone else (pending Michigan State's bowl outcome). Not every BCS champion could boast three wins over teams with no more than one loss otherwise. Maybe 12-0 Iowa wasn't deserving of the title of champion, but the College Football Playoff format would've made sure that 15-0 Iowa would've been.
Besides, it's not like the CFP has lost all exclusivity. I think most fans would've been fine with TCU or Baylor being crowned national champion had they made and won the playoff. Like '04 Auburn or '08 USC, those teams could've been seen as acceptable champions if they had the opportunity to win that title.
I don't want to see the playoff field expand beyond four. I am far more OK with leaving out potentially worthy champions like TCU or Baylor from 2014—or Ohio State, had the Buckeyes been left out for one of those Big 12 teams—than accepting an unworthy team as the national champion. I'd rather say "tough luck" to 2004 Auburn than accept the equivalent of a 9-7 New York Giants team as champ.
Going to an eight-team playoff will bring in the possibility of an unworthy team winning the championship. The 2015 Notre Dame or 2014 Mississippi State teams—each of which finished eighth in the final regular season selection committee rankings—wouldn't be the equivalent of a 9-7 Giants team, but leaving them out wasn't the equivalent of leaving out 2014 TCU and Baylor either. Their performances in the regular season left no doubt that they were not one of the absolute best teams in the country, so there is no reason to give them an opportunity to win the title of "champion" despite that fact.
In short, an eight-team field would weaken the college football's antibodies against an unworthy champion in one area without strengthening them in another, and that wouldn't be a good thing for the sport.