So now I FINALLY get to where we can start looking at 2013-14 to present as to the legality of the college football top-level national-championship farces which have masqueraded as entertainment for Football Nation America:
This is going to be substantially harder than the post previously-referenced. In 2013, there was an organized website (for which I thank the people behind the former "Football Geography" website for the information) which gave detailed information as to the probation and bowl ban status for the teams.
I will try, however, to continue up the line. This is a list of, for 2013-14, the BCS, and for 2014-15 to 2020-21, the New Year's Six, all the games under the purview of an on-field National Championship. Let's see how many teams don't make the cut:
(PS: I am willing to add to this at any time if people remember or discover inconsistencies. Please put in the comments if you find any.)
There are teams who could have permanent places on this list, at least with respect to reasonable sensibility:
Penn State.
Alabama. (if you wish to believe they should've been Death Penaltied at some point in the 2000s...)
Miami.
2014:
Rose: Michigan State 24 - Stanford 20
Fiesta: UCF 52 - Baylor 42
Sugar: Oklahoma 45 - Alabama 31
Orange: Clemson 40 - Ohio State 35
BCS National Championship: Florida State 34 - Auburn 31
Auburn is an obvious carryover from the previous season's farce with all the player payouts, etc.
Ohio State was in the final year of three years probation for the whole fiasco which upsot the 2010-2011 BCS.
Baylor was illegally recruiting players through a "female host program" from 2011-2016, as revealed in a 2016 major violation. This was actually the very beginnings of all the "Rapelor" stuff, according to the August 2021 decision on Rapelor, so NOTHING they have done in the CFP Era is valid.
2015 (start of the CFP):
Peach: TCU 42 - Ole Miss 3
Fiesta: Boise State 38 - Arizona 30
Orange: Georgia Tech 49 - Mississippi State 34
Cotton: Michigan State 42 - Baylor 41
Oregon, Florida State, Alabama, and Ohio State were in the tournament.
Baylor, previously listed.
Boise State was in the final year of four years probation for what they did to gain prominence in college football -- cheat.
TCU either was in the first year of or one year short of four years of illegal payments for work by almost three dozen student athletes in several sports. Unknown whether it would've made illegalities to make this or future appearances illegal, but it is to be noted.
Ole Miss: By 2017, over 20 NCAA violations had been found under coach Hugh Freeze and his staffers. Here's the list as of February 22, 2017. December 2, 2017: Two year bowl ban, one self-imposed. No wins vacated, but they should've been, so both this and the 2016 NY6 appearance should be voided. Wins from this season were vacated due to ineligible players, as were wins in five other seasons.
2016:
Orange: Houston 38 - Florida State 24
Fiesta: Ohio State 44 - Notre Dame 28
Rose: Stanford 45 - Iowa 16
Sugar: Ole Miss 48 - Oklahoma State 20
Alabama, Clemson, Michigan State, Oklahoma went for the title.
Ole Miss, previously listed, though no wins from the 2015-16 season were vacated, but the team never should've been in this position.
2017:
Orange: Florida State 33 - Michigan 32
Cotton: Wisconsin 24 - Western Michigan 16
Rose: USC 52 - Penn State 49
Sugar: Oklahoma 35 - Auburn 19
Alabama, Clemson, Ohio State, and Washington were the final four.
I think it no secret, and I'm willing to correct as it is discovered, that the NCAA has taken more and more of a back seat to the misdeeds of it's football programs. I'm accessing the NCAA's own databases, as well as relevant news reports, as I can find them.
2018:
Cotton Ohio State 24 - USC 7
Fiesta: Penn State 35 - Washington 28
Orange: Wisconsin 34 - Miami 24
Peach: UCF 34 - Auburn 27
Alabama, Clemson, Oklahoma, Georgia played the tournament.
To give you an example of the NCAA deliberately getting out of the way: As of 2019, this is the list of all teams bowl-banned. Only ten times since 2000 has a bowl-eligible team been banned. Two of those were Pedo State, a third was the Terrelle Pryor situation.
In fact, per Wikipedia: There are only nine FBS probation schools, in any part for football, at this point. Rapelor is the longest, until 2025. Notre Dame even is on probation this year, but for a relatively minor recruiting mess. Florida (impermissible contact after the 2019 Peach Bowl, though the situation does point to a consistent record of illegalities at the school), Missouri's entire athletic program, UTEP, Mississippi State, Pittsburgh (impermissible use of coaching staff, so that one could make a CFP appearance illegal if Pittsburgh wins the 2021 ACC title game Saturday), Akron, and South Florida are the others. There are NO current active bowl bans.
2019:
Peach: Florida 41 - Michigan 15
Fiesta: LSU 40 - UCF 32
Rose: Ohio State 28 - Washington 23
Sugar: Texas 28 - Georgia 21
Alabama, Clemson, Notre Dame, Oklahoma contested the championship.
Just saying for some emphasis right now: Between what we know of TCU, Boise State and Rapelor -- plus the COMPLETE failure of Scott Frost at Nebraska, is there ANYBODY left who believes that, within five years, we won't be putting UCF on this list? There's nothing there YET - and that needs to be made clear!!! BUT...
2020:
Cotton: Penn State 53 - Memphis 39
Orange: Florida 36 - Virginia 28
Rose: Oregon 28 - Wisconsin 27
Sugar: Georgia 26 - Baylor 14
LSU, Clemson, Ohio State, Oklahoma
Baylor, previously listed.
Florida, see above, depending on the nature of the consistent previous violations.
2021:
Cotton: Oklahoma 55 - Florida 20
Peach: Georgia 24 - Cincinnati 21
Orange: Texas A&M 41 - North Carolina 27
Fiesta: Iowa State 34 - Oregon 17
Alabama, Clemson, Ohio State, Notre Dame
Florida, ditto.
You could make a case for Texas A&M due to a fairly serious 2019 recruiting violation. Nothing Reggie Bush-level, but it's clear by the database, this had some heft.
I do reserve the right to add to this if any errors or additions need be made.