This technique does not sound promising to me but it might be worth considering under certain circumstances. If inside lawyers always had to obtain a written sign-off of their superior before they retained outside counsel, it would certainly make them think a bit more before triggering the cost.
My reaction to this idea is that it is belittling to the person who wants to hire outside counsel. If they do not have the judgment of when they should seek approval and when proceed on their own, the problem is more serious than outside counsel cost control.