Any fan of a current Big 12 school who wants to get into the SEC or Big 10 at this point is an idiot. From an actual fan perspective. Of course every single athletic administrator would fall all over themselves at the chance.
The Big 12 schools (and most ACC ones) should be focusing their efforts less on getting invited into those leagues and more about coalescing as a product that stays included on the field in major college football. You'll never get the payday, but if you get to stay part of the mix, it's as good as you can do.
The factors required for inclusion in those leagues going forward are fixed and in the past. You can't win your way in, you can't buy your way in. If you didn't start building your brand 50 years ago, or have been grandfathered in, it's over. There's no room for new money in that tree fort.
Tech has struggled in the Big 12 for the better part of the last 15 years. They'd fare worse in the SEC. They'd be fucking miserable. They could do the chant though.