#1 there are no phony majors, all States have Boards or Regents or Chancellors at the State Level to oversee Colleges.
The problem with CFB is obvious, if the players that Generate the Revenue got a small piece of the pie (money generated) that would balance the scales.
Instead it goes to Coaches, and if I was a Coach with a $8 to $11 Million dollar yearly salary hanging in the balance based on winning, then hell yeah I'd cheat too, especially since the NCAA is corrupt anyway.
Before you get your panties in a wad, if all P5 Colleges had a "carve out" for let's say $5MM to pay the REVENUE GENERATORS (FB & MBB roughly 100 players-stipends)
Don't call it a salary, cancel the full cost of attendance stipend, and instead have all NCAA P5 Teams give out these "stipends" to go along with the full FB & MBB scholarships for the P5 -- that's 100 stipends X $50K per stipend = $5 Million in yearly carve out Money.
With everyone at every college getting the same stipend (could be as low as $35K or $3.5MM total) , the Players are more likely to evenly distribute among all P5 Teams rather than loading up at a few Blue Bloods.
Title IX and other things will have to be dealt with, because T9 doesn't say you give everyone the same thing, the Law says equal access to facilities, but the law has been twisted into 2 Sports raising money and then those Monies get redistributed to sports that have equal access to facilities but cannot raise any money.
Regardless, as long as all the Money is concentrated among the coaches , there's no incentive for Players to spread out among the 65 P5 colleges.
BTW, don't let the colleges tell you they can't afford to give FB & MBB the stipends they deserve, coming off of a bad year due to CV19 , College Athl Depts are spending like King Midas while searching for coaches.
15yrs ago at Bama, Saban got $4million and his Staff got $4million total, now Saban gets $11Million and his on field Staff gets the same $11 Million (doesn't include 100 analysts behind the scenes)
In 15yrs Bama went from paying on field coaches $8 million per year to $22 million per yr, there has to be money for Players that generate the Revenues to get larger stipends.
This is the only way to balance the distribution of talented players - pay them the same stipend at all 65 P5 Colleges.
IMO this is the only way to save the Sport going forward.