Mississippi State is a SEC cellar dweller and great candidate to examine for relegation. This article shows that MSUs FY2024 revenue was $127MM against expenses of $134MM (deficit due to a COVID loan repayment). Football created $43.7MM. This number is ticket sales, sponsorships, concessions, etc. The SEC TV deal sent MSU $52.5MM, a number expected to grow significantly in coming years.
Currently MSU fields teams in Men's: Football, Basketball, Baseball, Golf, Tennis and Track and Field, plus Women's Basketball, Cross Country, Soccer, Softball, Tennis, Track and Field, and Volleyball. All sports other than football ran a deficit.
Let's say MSU gets relegated to the Big12, or something like it. Last year the Big 12 distributed $470MM to it's member schools. They did an unequal split for the new members that will equalize in coming years but if you average it, that's $29.4MM per school - and that's before the SEC revenues really kick into high gear when they add another game or play-in tournament for the CFP. That gap is not going to shrink.
If you take just the football TV revenue alone, MSU would lose $23MM/year. The reality would be much worse than that, because a moribund MSU fan base is not showing up for a football team that just got relegated and is now hosting a home schedule of Baylor and West Virginia. Their ticket revenues would crater as well, let's be generous as say that they only dip by 30%, which is half of the dip that Premier League teams take when relegated (even including parachute payments). That's a loss of another ~$14.5MM. The original AD budget of $127MM is now down to $89.5MM. What gets cut? MSU is relatively poor, they don't have a Boone Pickens to make up the gap. Student fees can only cover so much. And don't forget Title IX, you can't just cut women's sports. They'd scrap everything except football, baseball and (maybe) men's BB and the bare minimum women's sports they'd be required to keep. Even then, all those sports would take huge cuts.
Are these solvable problems? Sure, and soccer shows the way: ADs could negotiate relegation clauses in contracts, the NCAA could figure out the player employment legal jumble and work with the players to create a CBA that would allow for buying/selling player contracts, that same currently non-existent player's union could work with the NCAA to create conditions for transfer so that a relegated team doesn't immediately lose all of its players to the portal, conferences could setup parachute payments, etc. If there's a will there's a way. The problem is there is no will. Nobody is beating down Sankey's or any commissioner's door for relegation/promotion. In fact, it would be actively opposed by any team in the SEC or B1G today for obvious reasons.
So yeah, relegation is a total and complete fantasy in college football.