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

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").