Cecil Terwilliger, your point regarding the money to be made by the doormat schools is certainly correct, but I take issue with the reduction of FBS schools resulting in less profitability for the schools.
As it stands now, most FBS schools do not make money. Cite:
https://www.al.com/sports/index.ssf/...but_20_fb.html
Making even less money (and thus, losing even more money) might be good for such schools, as it would return the primary focus of the institution to education and not athletics.
Having football programs exist to, in large measure, get beat up on by other, richer schools hardly seems like an admirable or worthwhile endeavor. Yet such programs apparently are able to fill their rosters up with willing players, so what do I know?
In any event, my view of relegation is not a FBS/FCS split, and perhaps the relegation would occur over a period of years, such that if you have 3 losing seasons in a row, you get demoted to a non-championship division. Recruiting might suffer, but with scholarship caps, the most winning-est of schools can only take on so much talent, and the NCAA can put limit on the number of transfers allowed. Or we could just give up the whole "student athlete" fiction and start allowing schools to openly pay its players, and then let the free market work its magic.
In reality, there are only 15 or so schools that have a realistic chance of being the national champion in any given year, and the identity of those 15 schools don't change much. Why don't we just accept that fact and build the college football schedule (and associated divisions) around that reality?