Idea for replacing BCS in college football

As everyone knows and agrees, the current system for finding a national champion in college football is terminally flawed. In 2004, undefeated Auburn got denied a chance to compete for the championship because currently the two teams that get to play for it are determined by a computer algorithm that weights strength of schedule, margin of wins and other factors.

Here is my idea for a replacement system that would be absolute and much, much more exciting to watch. Teams would schedule and play their first 4 games as normal. After that, based on the previous years’ ranking of teams a massive, nationwide 8 game tournament would be held. The national champion the previous year would play the worst team from the last year and so on in the first game. There also would be a structure set up for the losing teams to continue playing games to determine their final ranking. Every team, even teams that lost every game all season, would still have 8 games through the tournament to determine exactly where they place on the nationwide scale. The final week would always be the most exciting as hype had built all year around the two teams that had remained undefeated all season and the national championship contest itself would be a massive spectacle with the only undefeated team emerging as national champion every year.

The first 4 games would be scheduled by teams’ athletic departments so traditional rivalry games could still happen every year, such as the Apple Cup, Notre Dame vs Michigan, USC vs UCLA, etc.

What do you guys think? Good idea, bad idea? What are potential issues with such a tournament system?