Does the board of trustees vote in the new president? If so, why wouldn't those folks want to bring a championship back?
So there's a Board of Fellows and a Board of Trustees. The BoF is who really has power. In short, there's a rule that a CSC priest has to be the President, and most of the potential candidates either dislike or are ambivalent towards football.
Jenkins at least wants a winning product. The next guy is more likely than not going to pull ND in the other direction. The good news is that Jenkins is unlikely to leave his post any time soon as he's done an excellent job with the
school aspect of Notre Dame (which, to alumni, is the most important thing).
The only way to get a more football-friendly administration would be through some crazy turnover in the BoF. You would be shocked how many people in that group are either anti-football or don't care about football, and it's really only the fact that so many of the big donors
do care about football that they've continued to try to be competitive.
None of this has anything to do with this situation except to say that if Jenkins/Swarbrick/et. al. were replaced it's unlikely the next leadership would be any better.