I have several decades of experience as a software engineer and have worked at several different companies that hired management consultants to rubber stamp decisions they had clearly already made. In each case, the company proceeded to deflect blame to the consultants internally, when employees got mad about the decisions. I have heard similar stories from friends and colleagues. So at least your skepticism about internal blame is unfounded.
I urge you to consider the ethics of your current employer and consider seeking employment with a different company.
Are you sure your experience really maps to McKinsey? There are countless garden-variety Office Space bean counter management consultancies that are called in as RIF shock troops etc. My experience with McKinsey is them being strategic consultants to C-suite where nobody is looking to "shift blame" or a docile rubber stamp. They're far too expensive if that's what you're looking for.
I don't recall if my experiences involved McKinsey or not. I do understand that not everyone looking for a rubber stamp needs to involve a firm as expensive as McKinsey, however I disagree with the general assertion that they're always too expensive for this.
If there are very large amounts of money or very risky behavior involved (e.g. behavior that could trigger an investigation by a government agency), it's sometimes worth paying for the best of the best, so you can avoid any questions along the lines of "why did you use JoeSchmoe's RubberStampsRUs Consulting, when you could have used one of the big firms?"
I can’t guarantee that my experience scales to the entire firm but this doesn’t really resonate. I’ve never come into a project with a day one answer. I think the archetypal example of what you describe is organizing layoffs, in which case the company needs to shed heads and needs to know where it can do so. Which is sort of a day one answer. I’ve never touched this sort of thing Personally.
I’m not sure who the rubber stamp would be for either. Your subordinates I guess? But that seems not particularly important tbh.
I'll just reiterate what I said above, I urge you to consider the ethics of your current employer and consider seeking employment with a different company.
I’d rather work on something I believe to be good at a big decentralized company like McKinsey than something like what many / most large tech companies do. There’s basically no relationship to the other parts of the firm
Sure, I get that it's a big company and that not everything it does involves selling people dangerous drugs that ruined their lives [1], while simultaneously consulting for the government regulators that regulated those drug companies [2], or aiding government corruption [3], or assisting dictators with their assassinations of pesky journalists [4]. But it's all the same company. I wouldn't want to work for big tech either, but to imply that McKinsey can be better than them in _any way_ is completely laughable.
I urge you to consider the ethics of your current employer and consider seeking employment with a different company.