How can it be that what you just wrote is such a widely known fact? I've been reading this and hearing this from consultancy people as well for many years now. If the guy lacks the political power, why don't his internal political opponents say, "nice try hiring the consultants, but we know this trick very well, you still don't get it your way".
It has to be some kind of higher level protection racket or something. Like if you hire the consultants there is some kind of kickbacks to the higherups or something with more steps involved where those who previously opposed it will now accept it if it's rubberstamped by the consultants.
Or perhaps those other players who are politically opposing this person are just dummies and don't know about this trick and actually trust the consultants. Or maybe it's a bit of a check, that you can't get anything and everything rubberstamped by the consultants, so it is some kind of sanity filter that the guy isn't proposing something that only benefits himself and screws everyone else.
And if it's the latter, then it is genuine value, a somewhat impartial second opinion. Basically there is a fog-of-war for all the execs regarding all the internal politics going on, it's not like they see through everything all the time and simply refuse to take the obviously correct decision for no reason.