Here is my case why is it is better for DB to hire the next coach and then step down.
Schlissel has no experience with big time sports. He may select an AD with little background in big time sports. I believe the AD hired by Schlissel will be asked to bring a clean cut coach who is not going to embarrass the school. I do not think the mandate would be to go out there pay as much as you want and hire a dynamic coach that can win.
For example, if
Jim Kelly, Urban and even Harbaugh were available, I do not believe the next AD would hire them -- too risky for Schlissel.
If DB is still around to hire the next coach, then I believe he will do whatever he can to bring a winner and money will be no problem (or almost). The next hire will be his legacy and he is as competitive as the next guy and will want to be remembered as a winner.
I think the best scenario would be for DB to stay for another year, bring a winner and then step down. I am very worried that the next AD would select a very conservative coach from a small time program (e.g., Ivy league).
Edit: My reference to Kelly, Urban or Harbaugh meant as examples of on field winners with some off field issues.