Prove that management has earned leadership. A company that outsources one function is just as likely, in the eyes of employees, to outsource another. I suggest that companies have corporate and departmental newsletters, community sports teams, discounted memberships with health clubs, and anything else that improves employee morale. It is amazing how effective a Friday pot-luck can be. Employees tend to learn about each other, especially those who work in different departments or at different levels.
Outside activities are a tool to find and build future leaders.
Also, it's a bit like having your father coach the team when your manager is coach. As employees interact, they will exchange ideas about products and procedures. In social settings, employees are more willing to express the negatives, which can then be addressed by management. No matter what people say, you cannot and should not leave work behind. I believe in training and lots of it.