Others have already pointed out that thesis defences and hiring interviews already use this format. I'm not an educator, but I can see some downsides:
• Unless it's recorded, you can't easily get another opinion on how to grade it, except from those at the event
• Some students will naturally be better at interview-style exams, independent of their skill in the relevant material. This is also the case with written exams, of course, but I imagine the 'skilled bullshitter' types might do better in an interview-style exam, and a nervous student might do much worse.
• I imagine it would be tougher on students who don't speak the language natively
• The 'imprecision' of a wandering organic conversation might make it harder for the student to know what to study
• Different students don't get the same exam, which might raise questions of fairness in itself, but it's worsened by that the examiner's mood is likely to change. (With written exams, an examiner can mark all students on the first question before moving on to marking the second question, to protect against this.)
• Physical appearance and deportment might skew the examiner's judgement. (This is widely believed to be an issue with juries, after all.)
• You can't hide the student's identity from the examiner, as a measure against favouritism. With written exams this can, and should, be done