Conferences used to be small enough that each team would play every other team. The team with the best record was then the conference champion.
Eventually conferences expanded such that it wasn't practical or possible for every team to play every other team. But the conferences were only at 10 teams, at most (the Big Ten and the SEC, for many years, the PAC since the late 70's).
Then when the Southwestern Conference (Texas schools + Arkansas) broke up, the SEC agreed to add Arkansas, and to balance things out they also added South Carolina, which had been independent for a while. They were the first conference to go to 12 teams.
They decided the fairest way to crown a conference champion was to split the conference into two divisions of six, have every team in the division play every other division team each year, and then have the two division winners play in an extra game for the championship. They thought that was the best and fairest approximation to a full round-robin.
This was all still before TV dollars really exploded. The SEC champ game started in 1992, after the expansion. It wasn't until some years later that conferences figured out that the champ game could make a nice chunk of extra $$$.
The rules at the time, which the SEC had proposed and were adopted, stated that you had to have 12 teams in order to split up and hold a conf champ game. So that's why the Big Ten had to add Nebraska in order to do so. Simultaneously, the PAC added Colorado and Utah to go to 12 themselves. (they were really trying to pull a huge coup and land Texas, and almost did it, but the deal fell apart at the end)
Then in 2014, with the Big XII mostly stable at 10, the Baylor-TCU debacle happened, in which the conference promoted both teams as co-champions instead of giving it solely to Baylor -- which had beat TCU in the regular season, but then lost to WV, both ended at 11-1, and had no conf championship game to play in to impress the CFP committee a final time and both ended up on the outside looking in. Art Briles famously lambasted the comissioner at the time for not declaring Baylor the outright champion.
The rules were then changed to allow conf championship games with less than 12 teams in the conference, so long as the conference required a round-robin schedule and then they would be able to have the #1 vs #2 ranked teams play in a conf champ game, which is what happens now in the Big XII and I believe the American Conf.
I think eventually here, we're going to see the rules scrapped and re-written again, to just allow conferences to get rid of divisions altogether and allow their #1 vs #2 teams to play in the conf championship game.
So, at the end of the day, the conf championship game will be fairly meaningless, and like Panthadad2 said in post#3, it will just be a cash grab.