Geographically, the Pac 12 makes perfect sense for BYU. The conference already has Utah, Colorado, and Arizona schools so the distance would not be an issue. Also, the Pac 12 really lacks historic programs. USC and UCLA are the exceptions to this, but not very many people can tell you the history of Stanford, Washington State, or even Utah football.
The Pac 12 gets picked on a lot in college football for not sending teams to the Playoff or having success in the postseason.
Why BYU could get invited: It just makes sense. If the Big 12 were to go to 14 teams, the Pac 12 would almost have to since they would then be the only one with less than that. Honestly, out west if they want to keep their footprint in the same states/area as they are currently, BYU is by far the best option to pick up. The Pac 12 with BYU and Boise State or San Diego State added would help the conference, something that is not easy to do by adding G5 teams.
This would also renew and fix the BYU vs Utah rivalry game, would bring in some history and wouldn’t hurt recruiting since BYU has a unique market (LDS athletes) as it is.
Finally, with a new the Pac 12 Commissioner, the overall culture of the conference may change in BYU’s favor.
Why BYU won’t get invited.
Politics. The Pac 12 has said over and over that they don’t agree with how conservative BYU’s values are with the honor code and less progressive views with the LGBT community. Also, the Pac 12 doesn’t seem interested in “Football only” agreements and likely won’t budge on Sunday play in other sports.
Even though in every other way this conference makes sense, the discussion hasn’t really ever been there.
Chance of happening: 5%