I don't think anyone really answered your question. I work at McKinsey and can try to provide an understanding of how we add value. I have a PhD in computer science from a T1 university, so I'm not exactly the MBA type; but I am on the exact same track as them as a generalist consultant (called integrative).
Here are the good parts:
1. We are pretty good at being translators. For companies I serve, making sound business decisions requires understanding of the technical details. However, most of the time, the C-suite will not dive deep into them (most have no time; some just refuse to learn). Our job is to distill the complex topics into something that is digestible for everyone, and I mean everyone. The time spent by an analyst or associate is mainly on slide-making for this reason - there is a lot of iteration until the message and storyline are perfected.
2. We provide a voice for the technical working teams. Pretty much every project I worked in, the technical teams have a pretty good understanding of what they can do and what they need, but this doesn't always get heard by higher-ups. Part of our job is to relay these thoughts (again, in a digestible way) - anonymously if need be. Most of the time a representative of the client team also joins our C-suite discussion, which is a great career opportunity for them.
3. In addition to point 2 above, when the technical teams don't know what they need, we build out a plan for them. I built financial models, workplans, capability assessments for e.g., cloud migration for automotive part manufacturers (i.e., high-tech but not necessarily computer savvy companies) directly collaborating with working teams. They can then use these to present their case to higher-ups, enabling them to actually get what they need.
4. We have an understanding of the industry overall, because we go around and see what's happening everywhere. In order to prevent unintended spillage of company secrets, we get "conflicted out" of working with direct competitors when we serve a client, but we can work with different parts of the supply chain. We also have industry experts, internal and external, who can provide insights - which is sometimes very critical to get up to speed quickly.
The burnout is also real, and I am actively trying to move on to a "real" tech job after approximately 2 years at the Firm. But positive client interactions are very fulfilling, and I have learned so so so much about so many different things, it's incredible.
I'm also pretty lucky to have worked mainly in growth or go-to-market strategy. I have never laid anyone off, never led to someone losing their job whatsoever (I actually kinda did the opposite once by helping them overcome a PIP), never participated in political battles, and never did anything that could be considered unethical like the Purdue thing. Just solved cool business problems for tech companies for 4-8 weeks at a time.