I worked and interviewed a lot of people in business consulting. We did ask what you call Fermi problems as they are surprisingly representative of the abstract thinking that is required in the job, specifically proposing frameworks for what kind of information we need to either go and get or state as assumptions in order to support a decision. As the GP points out, the questions are testing how you model something you don't know but have common sense about, and significantly, how you don't get caught up in uncertainty or irrelevant minutia and identify some core assumptions.
That said, I agree 100% with you about "trick" questions. It seems some people cannot distinguish between "market sizing" (Fermi problems) where you need to make reasonable assumptions and describe a model of something, and "a man is found in scuba gear in the middle of the forest" brainteasers for kids. I have no idea why anyone asks brainteasers in an interview.