How is this not what is currently the norm? How do dissertations work at your university, if they are not exactly this?

For PHDs yes. Everyone else takes written exams. Highschool needs this hard.

Ok. Here the equivalent of high school final exam also includes oral exams. But I don't see how written exams are problematic regarding AI-driven cheating. You only have pen and paper and depending on a subject a verified calculator or a provided dictionary. Also cheating with a paper is way easier and has higher odds of succeeding than trying to hide an electronic device.