McKinsey was doing some work for their dept. I asked him what they did. He said, "McKinsey asked us for lots of information. Then they put it into a dossier and gave it back to us."
Information is siloed, teams compete rather than cooperate, any team's own dossier is going to be seen as biased and unobjective.
There's real value in hiring a neutral, competent vendor to come in, assemble the relevant information using best practices, and present a "dossier" with common-sense conclusions. Then the leader who hired them can use that as political cover for taking the necessary actions they wanted to in the first place, because the leader is no longer siding with one bureaucratic faction against another, but merely taking objective advice from an outsider.
That's actually worth a lot.
That looks like three deeper problems than the consultants were tasked to solve.
(Not only do you have counterproductive, misaligned culture; but even the CEO can't/won't fix it; and the CEO even has to play political games, just to work around the bad culture, for smaller goals.)
No, this is exactly the reason the consultants were hired. Not to solve the cultural problems, but to work the broken process. It's not really in the consultants interest to solve the cultural problems anyway, because it drives repeat business.
There is big money in doing that too - you gain a client for life if you're successful, and you get to recommend all your friends in Professional Services companies who give you a cut/forward strategy business your way.