You can't make it a requirement unless you include ALL conference champions
And, no, it would encourage every team to play weak non-conference games. There's no benefit to playing a strong team before conference play because it can hurt you.
If a conference title is a requirement then ND & BYU can't go--there's no exceptions to requirements.
There's year's where the second best team in a conference is more deserving than a conference winner. It was true with Penn State vs. Pac XII/Big XII last year and it was true with Bama vs. Pac XII/Big Ten this year.
This post is incorrect.
1. All conferences need not be included. This championship is called national, but it is the power 5 national championship.
The argument that all conferences must or should be included is as accurate as arguing the NFL should or must include semi-professional League champions.
If there was any forward thinking among the non power-5 conferences is they would put together their own championship playoff.
2. Since winning a conference championship would be a prerequisite there is no downside to playing and possibly losing to a strong nonconference team. As long as there are 5 conference champions looking to squeeze into 4 spots, there will always be incentive to play a stronger OOC schedule.
3. As far as ND goes, there could easily be a provision that allows a highly ranked Notre Dame to be considered instead of the ACC champion.
4. At no point can you objectively argue a 2nd place team from any conference is more deserving of another member's champion. The eye test is bullshyt. The eye test simply allows a bunch of clowns to argue that their opinion is more important than objective data.
Another consideration. Alabama wasn't even the second bedt SEC team this year. They were the 3rd best team, behind Auburn and conference champion Georgia.
Last season Ohio State at best was the second best team in the Big10, and possibly the 3rd best behind Wisconsin. When given the opportunity to prove otherwise Ohio State showed themselves to be what they were. A Big10 also ran.
The eye test allows people to interject their personal bias.