Clarification for non-Danes: this post is not entirely accurate. Not all Master's courses in Denmark have oral examinations, and many courses before the Master's level (including elementary school) have oral exams. It is unrelated to the academic level, and instead related to the academic discipline and the size of the course. The latter is in my experience the main constraint, as oral exams are difficult to scale. They usually take 20-30 minutes per student, and if you have a course with 200 students, well, you're in for a long time.
The oral exam format described is also somewhat unusual, in my experience. It is usually the case that there is one internal examiner and one external examiner in the room. More than that would be ruinously expensive. The format varies; usually it's a combination of a short presentation and questions asked by the examiner. Drawing a random topic is very common.
Source: I am a university teacher in Denmark who teaches master-level courses without oral exams, and I have been an examiner for many oral exams at university level.
There was an interesting talk I heard a while ago about the scalability of oral exams vs written. They did quite a bit of study of typical exam preparation and marking times and the cross over point where oral exams were actually taking longer than written exams was surprisingly high, around 180 students or so. To be fair though I think they considered 15 min oral exams, but the gist is that in the scalability argument people tend to forget to account for marking and exam design time appropriately.