You don't need to read to the end. I'll put it here. They're bullshit.
They are the natural complement to post-season conference basketball tournaments, which -- with one notable exception -- sprang up in the 70s after the NCAA expanded its basketball tournament to let in conference runner-ups (or, as I'm sure Pete Arbogast would say, runners-up). Historically, the NCAA tournament was limited to champions of accredited conferences and at-large teams. The at-large teams were either independents or members of conferences too small to qualify, as was the AAWU in the early 60s when it only had five teams. But the NCAA left it up to the conferences to determine how each one selected its champion. The ACC was the only conference in the 50s and 60s to hold a post-season tournament, and the winner of the tournament was the conference champ and became the only ACC team in the national tournament. There were seasons when an upstart won the tournament and a really good team had to stay home. Once the AAWU became the Pac-8, its teams no longer qualified for at-large berths.
When the NCAA decided to let in non-champions, most of the conferences came up with the idea of having a post-season tournament to determine the conference champ. Their goal was to get an extra team into the NCAA tournament (thus a bigger share of the tournament revenue), so the [always unspoken] hope was that an also-ran would win the tournament and the regular-season champ would snag an at-large bid. Another byproduct of this was that the number of independent teams shrank dramatically. With independents now competing for at-large bids with conference also-rans, new conferences sprang up to ensure their members would receive at least one automatic bid.
Once the NCAA expanded the field to 64 teams, and likely before then, conference tournaments became meaningless except as content for ESPN, revenue for the conferences, and a last hope for a 15-loss team to make a run and get invited to the dance.
In football, conference championship games started in the early 90s for two of the same reasons: content for the networks in early December and revenue for the conferences. It coincided with moves to create a "true" national champion, that is, to eliminate the split national titles that occurred during the traditional Bowl Era. In theory, the winner of the CCG would get a more desirable bowl bid. But by the time the BCS came along at the end of the 90s, CCGs made little sense, and when the CFP expanded the "playoffs" from two teams to four, they made no sense. Witness the teams that made the playoffs without even participating in their CCG, both under the BCS (Nebraska, 2001, and Alabama, 2011) and the CFP (Ohio State, 2022).
With a 12-team playoff now, the only point of CCGs is seeding. That's not a good enough reason, in my view. They are bullshit.