No, they should have one of the best teams with 1 loss play the participating undefeated team and then vote, assuming said undefeated team loses.
If they win, problem solved.
The whole thing is as corrupt as the Harding administration, but that's typical of the NCAA's 21st century brand of neo-professional sports.
The NCAA has nothing to do with administration of the bowls.
As a
matter of fact, antitrust concerns keep the NCAA at arms length from having anything to do with running the bowls and specifically from establishing any sort of playoff contest, which is viewed as a specific threat by the bowl interests.
In other words, even if the "neo-professionals" at the NCAA wanted a playoff, they'd be squashed in their tracks by lawyers at the Walt Disney Co and those representing the 28 independent bowls.
The NCAA runs a football "national championship" tournament, the schools are not obliged to play in it. They could still opt to play in bowl games. I don't think the NCAA should be concerned about antitrust issues. Besides, each playoff game could be held at one of the existing bowl venues and be organized by the existing bowl committee.
The NCAA brings in about $450 million a year in revenue and distributes that among its member schools and the vast majority of that income comes from the CBS TV contract.
The football bowl games brings in ~$200 million per year. If the NCAA wanted to start a D1A football playoff, they'd first need to find a way to replace that $200 million per year of income that the bowls are currently throwing at conferences and schools. That's a tall order in and of itself.
The 28 bowls are actually in the business of raising money for local uses, and their payoffs to the schools and conferences are merely the cost of raising this money. Collectively, they view a playoff system as a threat because it threatens their ability serve their hometowns. They already have a Supreme Court antitrust ruling in their favor that serves as the basis that precludes the NCAA from moving in on 'their property'.
The bottom line is the bottom line.