You can also simply apply cold. Ultimately turned the offer down due to concern about burnout, but I had a great experience interviewing with McKinsey. Compared to most tech company interviews, I felt like I was given every opportunity to showcase my strengths as a generalist, and the people I spoke to were all very likeable and invested in the process.
There's a difference between working as a consultant for a body-shop (no offence - and I do appreciate that McKinsey is nothing like Accenture) compared to doing consulting under your own name though.
Out of curiosity, what would you have been doing under McKinsey?
I think a lot of developers would prefer to sell themselves on their ability to take high-level business problems and work with a team to come up with software solutions, rather than just their raw technical skills. Of course, it's important to understand the details too, but I get more excited by delivering solutions which make my customers' lives easier than implementing a low-level algorithm that already exists in a library somewhere anyway.
McKinsey case studies are more similar to real work than most interviews. You're given a large business problem, and then you're responsible for demonstrating the sorts of questions you'd ask a real client in order to do product discovery and get accurate requirements. Then, you talk about the way you'd architect a solution and go into the details if you have time. At the end of the interview, your interviewer asks you realistic questions like a client would.
I do like pair programming exercises (the ones where you get a realistic problem with an open-ended solution, not the type where the interviewer yells at you until you get the One and Only Solution). And McK does a bit of that too, with questions which validate your ability to develop across the stack, but aren't anything you wouldn't encounter in a normal day at work ("implement a JS component in whatever framework you want", "given this table structure, write a query to do X in whatever SQL dialect you want", "implement a basic REST API to fulfill this use case in whatever language you want").
