I think the manager and the coaching staff all have different jobs, as a necessary division of labor.
At the major league level, coaches aren’t exactly teaching players anything about the game of baseball itself as much as they are spotting things players are doing wrong, or whether players have gone out of sync, or helping players work on a particular skill they’re trying to acquire, or preparing players specifically for this team/this pitcher/these hitters we are facing today—stuff like that. Coaches’ job is to guide players in these ways and provide feedback to them as they go.
The manager, to your point, is focused more on managing the players’ expectations, state of mind, in-game trigger time, etc., but they also provide the coaching staff the guidance they need on what to work with the players, and what the expected successful outcomes should look like. In that sense, the manager is the executive and the coaches are his officers. In a cohesive organization, the front office and field manager work together on establishing goals, objectives, and strategies, and the manager distills all that to the coaching staff who distill it further to the player level.
That’s the way a winning organization should probably behave, at least, and after years of not doing that in a way that was obvious even to outsiders like us, the Tigers apparently have finally figured out how to do it right. And look what’s happening.