Pardon me and my ignorance, but this seems so totally ripe for a highly competent consultancy to come in and deliver excessively amazing value compared to ... others.
Because this consultancy would first need to become golf buddies with its clients senior management, at which point it would be just like every other consultancy.
The whole consulting model is broken. Third-parties can never replace employees for the simple reason that their interests are misaligned. The most you can get from outsourcing is a boost in this quarter's figures (which is enough to get said management their bonuses, and then they move on!).
Why doesn't that happen?