I would like to see some of the top-tier private school coaches take over a mid to low-tier public program and see how long it takes to create their "culture" of winning.
To my knowledge it has only been done successfully one time in recent history. It took five years.
Mike Fitzgerald had a two-year run as head coach of St. Francis for the 2014 and 2015 seasons. He compiled a 15-7 record and took the 2014 Spartans to the 6A semifinals.
After two years of not being a head coach he took over the York program for the 2018 season. The prior season, 2017, York had a 1-8 record. Their only win was over Proviso West, I think by nine points. They pretty much got pounded by every other team they played.
Mike Fitzgerald's six-year tenure at York went as follows:
2018 (4-5)
2019 (4-5)
2020 (4-2)
2021 (8-2)
2022 (12-1)
2023 (11-2)
So it was in his fifth season at York that he matched his success at St. Francis by reaching the semifinal round of the playoffs, in this case in 8A.
I raise this example merely to be fair. It was done once. Your point still remains valid. Such a transition is almost unheard of.
Mike Fitzgerald is, of course, now at Marist. He certainly qualifies as a "top-tier private school coach".