The difficulty becomes that, in a bad organization, a good manager can easily get stuck unable to both be a good leader to their team and be a good manager as seen by the organization. I've had multiple managers fired/reassigned because they were leading the team well in a fractured organization, but because they weren't prioritizing the things that upper management wanted over the objections of their teams.

If what the team wants to do to succeed is at odds with what the organization thinks it wants, the manager often can't square that circle.