There are many high quality teams that have little chance to win their conferences that will need to beef up there schedules to get the 3 open spots. And a team that loses in their conference championships (whether we still have those games or not) could get a 2nd shot at the big prize by having at least one quality game against a non conference team.
If they keep the conference divisions, for example, any team in the SEC West, any team in the Big 10 West, any team in the ACC Coastal, all potential losers to the "powerhouse" teams in their conference would be in prime position to get one of the three open spots assuming a decent OOC schedule. Iowa State, Okla State, West Virginia's of the Big 12 are always going to be pissing into the Texas/ Oklahoma monoliths in conference would benefit from a high quality OOC game. You don't think Stanford and USC would still like to keep ND on their schedules.
And any team that wants to get attention, ala UCF, Houston and the like, would be prime targets for ND to get a quality game in.
I also think they could build in simple hurdles to prevent bad conference champions from getting auto berths. For example, make being rated in the Top 12 (or Top 10/Top 15) as a minimum to get an auto berth. In addition, you would still need some kind of seeding process with a 1st round being played at the top 4 teams' home field, their would be plenty of incentive to play quality OOC game to get home field in that 1st round.