You need a USC/Oklahoma/Clemson/Alabama in order for the conference to be respected on a national level. "Parity" and "competitive" become pejoratives if there isn't a heavy-hitter that can hang with the best in the country (think of how we have mocked the Pac-12 for it's "parity" as USC, Stanford, and Oregon have fallen off).

If Oklahoma State, Cincinnati, or Baylor can consistently get to the CFP/win big bowl games, I think the conference will be fine. If it's just a bunch of B and B+ teams without a clear A or A+ program, I think the conference will ultimately struggle with perception issues.

Not to say that the Big XII would be alone there - the ACC and Pac-12 are having the same issues - but the new Big XII won't have any name brands, so the margin for error will be much more thin.