It is difficult to overestimate the need for courage in managers and leaders. This short but powerful article by Gallup identifies some of the damage done to people and businesses when they fail to act and speak with integrity: https://bit.ly/AspireMCL077
How can this quality be developed? By having the senior leaders model it, communicate its importance and hold managers to account for delivering it. Rewards including promotions and bonuses should be contingent on the managers' ability to make or relay tough decisions, communicate them compassionately but clearly, and have the courage of their convictions.
A key success factor is their workload: whilst there will sometimes be additional burdens the workload must be manageable and they must have the support of their bosses to deal with unusually high pressures. It is also important for them to understand how best to relate to their teams and other stakeholders in ways that will cause them to be more willing to engage. Tools such as SDI2.0 and DiSC can help here as they provide information on preferred behaviours, core motivations, reactions to conflict/stress, etc.
Ultimately, businesses and other organisations should be working to create leader-managers at all levels in the organisation in order to realise the powerful and sustainable competitive advantages they bring (including the many benefits associated with higher levels of engagement). A culture of courageous integrity is fundamental to success in doing so.