Its hard to track down USC's revenues, because they are private, so I dug through their Title IX filings. Reading it one way could show USC does have a bit of a money problem. When looking at football revenue, at $53M reported in a pandemic year, they were barely above Iowa State ($52m), and far below the big boys who make over $100m. Now, the Pac12 got shorted games last year, but Oregon pulled in $77m. (for reference Arizona made $38m).
That being said, they allocated $56m of revenue to "non gender/sport revenue", which leads me to believe its more of an accounting issue than financial.
In total numbers, they don't really need money and make so much off donations that they're solid. So the question becomes, is money the primary driver?
For Texas and Oklahoma, it was not, not matter what anyone says. You could remove all of the media revenues that Texas makes in a year and they would still be in the top five of total revenues. Their football team alone makes over $140m a year with only $40m in expenses. They are also in no threat to lose money any time soon with the support structure they have built into their university. So if it isn't money, why?
Exposure and Recruiting.
While TCU could make the argument, I don't think its a secret that the only school that really benefited massively from realignment in 2010 was A&M. Their wins and exposure have shot through the roof and that has impacted recruiting, where they are nabbing more of the 5 stars that Texas used to strong arm by just saying "we are Texas". Now its "Play for the SEC"
This massive increase in exposure for the rival is what drove the move. It doesn't matter if the Big 12 gave them all of the revenue, that doesn't help win the recruiting battle. By moving to the SEC and "if you can't beat them join them" mentality with the HS coaches, they should be able to "we are Texas" again.
Oklahoma, much like them moving to the South when the Big 12 was formed and destroying the OU/Nebraska rivalry, is going to go where Texas goes. The Red River and the Dallas pipeline is far to important to Oklahoma to give up. As more SEC schools are feeding on Texas, Oklahoma needed to work harder and they need access to bigger and faster D-linemen to change the narrative.
Either way, this move was about more exposure and winning recruiting, period.
So look at USC, could they use more exposure? Yeah, probably. Last year wasn't their shining moment. But are they losing recruiting battles? Not really. They own SoCal and being in the Big Ten isn't going to help that. They also already play a pretty solid non-con with games against someone big and ND every year, so a scheduling alliance won't really do much. What they need to do is win, so where can they win the easiest?
This west coast to the Big Ten conversation doesn't make a lot of sense to me, especially with the relationship that the Big Ten and Pac 12 already have for generations. I think it makes more sense for the Big Ten to shore up the Pac 12, hold hands more so they do a game or two cross over every year, guaranteeing USC a rotation of Michigan, Ohio State, and Penn State, agreeing upon more academic/higher access governing rules, and strengthening the position of the Rose.
Keeping the Pac 12 alive gives the Big Ten a puppet state with 2 votes over the SEC's one. Its a smarter move over all, especially when you value more than just football revenue.