Wow! That is a very high percentage. I would imagine it would depend, somewhat, on the organization or company. I spent a great many years in senior management of a large non-profit--the pull on your time from so many directions would, on somedays, make it next to impossible to engage where you really wanted to. You are all things to all people and most of the people don't care that you are running as fast as you can. I had to make a effort to have meetings (not for the meeting sake) but to gleen information and "engage" not only in the objectives, actions steps and goals, but to "engage" in the personal and professional lives of my staff. When they felt cared about they met the objectives, goals and action step and made sure you were informed every step of the way.
I think there are managers and executive in some organizations/companies that are paid large salaries and are used as "window dressing"... it's not the intent for them to "engage" in organizational objectives.