I feel like this is because school, especially college, and particularly exams, is about as high-stakes as most people's lives ever get, so they look back at that time as peak-anxiety. Think about it: you're being evaluated and the result of that evaluation shapes the next step in the pipeline, and ultimately the trajectory of the rest of your life! Well, at least that's what the university officials, professors, you…
I usually learned the most out of take-home exams. You’d usually need to study and brush up on things, but then having a week to thoroughly work out everything was always a great learning experience. It is a way of the professor saying “you should know this and if not, know how to figure it out”. It was an actually good test of your knowledge and skill and didn’t rely on being able to spit something out in one or two hours in a stressful environment.
I think you’re right that no adult experiences moments like you get in school exams. Almost never are you required to know some relatively arbitrary thing or solve some problem within an hour or teo. There are crunches and moments of needing to fix something quickly and important presentations, but in every case you are presented with something you already know about or have day to day experience with. And failure is usually not some drastic adjustment of your future. If the professor is not good, which is the norm, then exams are a bit of a toss up.