I agree that schedule strength will make a big difference for those six at-large spots, where you have - post conference championship games - a pile of two- and three-loss teams.
Looking at the CFP rankings for 2021, 2019 and 2018 - I tossed out 2019, just too much noise - here are the final CFP rankings pasted at the bottom - I just included 1 through 15. In 2021, top six conf champs would be numbers 1, 2, 4, 5, 6, 7. All else held equal, GA would move from 3 to 5, and you'd have three SEC teams. In 2019, 1-4 are all champs so no change there (treating ND as the ACC champ), and four SEC teams are in (I know there would be an argument of a three-loss aubrun in over Bama...). In 2018, more of a jumble. An undefeated ND is bounced out of the top four (they cannot get a bye as an independent), replaced by no. 6 OSU. ND would be 5, GA 6, and four SEC teams get in. 2017 would bounce swap Bama and OSU, and we'd have three in.
Given the rankings each year, I don't envision a 12-team field with less than three SEC teams each year.
RTR,
Tim
2021
2019:
2018:
2017: