The executives who hire McKinsey are often not clueless, but they often lack the political power in the company to push through their plans. So they hire some well-regarded business consultancy to get an "objective" analysis what needs to be done.
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.
My hunch is that in fact they won't agree with just any idea. There is a limit to how extreme the idea can get, though probably the filter is indeed weak. Still, without this filter, people would propose even wilder ideas that maximize their own expected payoff at the expense of other players, so just the fact that it has to be signed off by an external party is still enough information for the powerful decision makers that they are willing to fund their services.
Look at NEOM in Saudi.
McKinsey took 130M in a year to recommend a 500B investment in a 105 mile city in the desert. Sunk 50B and project was revised to take 50 years and 8 trillion.
It's impressive salesmanship how they were able to bilk such a large sum and support interim approvals for the regime to launder favors. I can see people wanting that "conflict."
Aside, there's a lot of stuff online re McKinsey. I suggest searching HN plus also search "Confessions of a McKinsey Whistleblower" in your fave web search engine.
My favourite was the LRB article "When McKinsey comes to town" -- see https://news.ycombinator.com/item?id=33869800