It is not coaches that create the atmosphere. A coach who views their program as more important than a university's educational mission and ethical boundaries, in a sane world, would be fired on the spot. The atmosphere is created by the trustees, and the politicians who appoint them, who allow coaches and ADs to chase money and wins instead of integrating their programs into the university.
Your theory is that Trinity and Yale don't have these issues because they hire less power hungry coaches and ADs. Nonsense. Trinity and yale don't have these issues because their coaches and ADs know that, while winning is part of their job, everything else is not forgiven so long as they win.
Those last two paragraphs, by the way, have nothing to do with Randy Edsall whatsoever, thought I doubt most of his detractors will be able to see that. If the NCAA gave a crap about protecting players from coaches leaving, as opposed to protecting their powerful institutions from doing whatever they want to do at the moment, they would simply say, as any pro league does, that you can't talk to another team's coach until his season is done. Period. To blame the coaches because the system forces them into this awful Hobson's choice of abandoning their players before the bowl game or leaving in a nanosecond afterwards is, frankly, idiotic. Are baseball managers more ethical than football coaches because they don't negotiate their next job while they're still employed? You really believe that? It's that their system, in this case, has firmer ethical groundings.