Airbus - Unless there is empirical proof that lopping off the top three tiers of management will improve things, you may not like the results of what you do. There may be some really good managers in the levels you would love to get rid of, and some really bad apples. I guess it's a question of knowing which apples are good and which are bad.
In cases like this it's choosing between the devil you know and the devil you don't. I'm not sure which is worse TBH.
S.