Yes, that specific thing happened just last year with Ohio State. They lost the last game of the season to Michigan in Columbus by 22 points. It's true that Alabama lost by 10 at home (to another playoff team) and made the playoffs. However, for comparison, the following teams still made the playoffs as well.
2014 Ohio State got in after losing at home by 2 TDs in week 2 to a Virginia Tech team that finished 7-6. Ohio State won the national championship.
2015 Alabama lost at home to Ole Miss by a touchdown. Alabama won the national championship.
2015 Washington lost at home in November by 2 touchdowns to USC.
2016 Clemson lost at home in November to Pittsburgh who would finish 8-5. However, that was only a 1 point game. Clemson went on to win the national championship.
2017 Oklahoma lost at home by a touchdown to eventual 8-5 Iowa State.
2020 Notre Dame lost by 24 points to Clemson in a neutral site contest in the last game of the year.
2021 Georgia lost the SEC championship game by 17 points to Alabama. The next month they beat Alabama by 15 to win the national title.
2022 Ohio State lost the last game of the year to Michigan in Columbus by 22 points.
Yep. Which shows that Georgia got screwed, not FSU.
I get why they felt they couldn't leave Washington out because of viewership/money because they beat Oregon to stay undefeated, even if their schedule wasn't much tougher than FSU's.
Just tells you it's not about the 4 best teams when money might get in the way.