I sometimes think that large organizations should have a group of "monks." These monks may be retired or they may still be drawing full pay. They would be male and female and from all levels in order to prevent too narrow a view. Some may even be from outside of the organization. There would be no more than twelve. Some secluded offices would be provided. A few could serve as monks and then return to full service but that would be rare.
Their job would be simple: Study, think, and argue. Advise any manager who seeks your assistance. Consider how the organization can be improved and what needs to be confronted now in order to prevent a crisis later. Surface what everyone knows but no one speaks. Make recommendations when you feel they are appropriate but most of all, make your presence matter.
My guess is the organization would benefit greatly.