I didn't say coaching doesn't matter; coaching, especially in terms of player dev, matters a ton. You're putting words in my mouth.
What I am arguing against is the idea that a managerial change is anywhere near the top-10 reasons why the Philadelphia Phillies, or any team, begins winning. Whatever slight psychological change it creates is entirely masked by things like data regressing to the means, schedules, etc.
Don Mattingly didn't make Christopher Sanchez pitch 42 scoreless innings. Getting to pitch against SF, the As, the Reds, the Rockies and the Padres did that. Sanchez may tell you it's because Don has created a looser clubhouse, but it's almost assuredly because he's good and those teams can't hit water if they fell out of a boat on top of positive luck (anytime you go 42 innings pitched without a run you're getting the benefit of luck, too).