Just to nit pick, I believe it's common knowledge that the result of the BTT Championship Game is too close to the Selection Show to be considered. The two teams playing have already been seeded. If a team like Nebraska would not otherwise make the NCAAs unless they won, the Committee simply marks one 11- or 12-seed or something to be booted in favor of Nebraska should the Huskers win the BTT. The BTT Championship played on Sunday at 2:30 pm CST exists for one reason and one reason only - absolute ratings gold. I don't know about last year, but Illinois/Ohio State in 2021 was easily the most viewed game of the regular season that year, and Illinois/Iowa the day before was the second most viewed.
I will always take winning the BTT (it certainly didn't "tire out" our 2005 team!) and another banner, personally ... win the games you play! With that said, if our stamina is for some reason such a concern that we absolutely need more rest than that before the NCAAs, I think the sweet spot is making the BTT semifinal then. I also selfishly want that to happen so I can attend the game.