Yours is a wide-spread sentiment... put the best four teams, not necessarily the four highest-ranked conference champions. The problem with that is that implies that a team that "looks" better to us somehow managed to lose their conference championship. So you are ignoring on-field results in favor of the eye test. Well, if you're going to do that, then why not do it for single-game results, too?
Say a dominant Alabama team ends up playing a lucky-as-heck Washington State team in the national championship. Washington State wins a close game. Alabama ends up with 1 loss, and Wash. St. still has its 2 losses to Eastern Washington and Boise State. On your logic, you could say, "look, even though Wash. State won the game, on balance I think Alabama is the better team, and therefore I think we ought to give Alabama the national championship anyhow." I hope that sounds ridiculous to you...?
Football is the most-complicated game in the world, and you decide the winners and the losers according to how well they play within those rules. One of the rules should be that if you aren't the best in your conference, you aren't the best in the nation. And if any conference doesn't like the possibility of Louisville (for example) not making the playoff... then let that conference decide that a poll or a vote at the end of the season will decide who its conference champion is. ...That's exactly how we picked national champs for decades, and precisely the problem the CFP is designed to solve.
Having clear rules in place that decide who gets in and who doesn't is the very best way to ensure that the winner is decided on the field, and not according to the prejudices and biases we all have. Remember how FSU would keep getting a high preseason ranking throughout the end of Bowden's career... and then tank and end up 7-5 or whatever? The whole point of the CFP is to stop letting those biases determine our national champion. Making only conference champions eligible would further that goal.
