I have, yes. My university experience ran the gamut, in that I had both classes in a massive lecture hall of hundreds of students where most never spoke a word to the professor and all exams were done via scantron, as well as small graduate courses of around 4 students where the entire class was oral exams and one-on-one demonstrations and group discussions. The smallest course was only available at all because of a particularly passionate professor who insisted on holding it, and the class was never available during semesters where he wasn't available, because nobody else was willing to put in the work to personally administer the class. Notably, all those courses cost about the same amount of money per credit hour from my perspective, so the university was making orders of magnitude more money on the large class (where I can't see oral exams being feasible without significant investment) than they were making off the small class.
> You can delegate to grad students, but the same can be said of oral exams
It's much harder to delegate an oral exam than a written one. As you've mentioned, oral exams combine administration with grading, which means the grad students who are delegated to need to be able to administer the exam (ie, effectively probe the knowledge of each examinee) as well as evaluate their responses. In a written exam, the grad student only needs to evaluate the responses, usually against a set of predetermined criteria since the structure of the questions is set in stone.
None of what universities are moving towards is better, but I fail to see how it isn't cheaper.
But what if AI conducts it?
The point is that the written exam is largely outsourced to PhD students here. The professor only looks at the model solution before and the grade distribution afterwards in extreme cases. Also you can parallelize the grading so that even for 300 students the grading is done in a week. Typically the professor spends half a day otherwise it would be 2 month...
I only do oral exams for my course and I am very happy how well it works. I normally ask students to grade themselves afterwards and I am typically spot on (I have written down the grade before).
For example, oral exams are still very common in Poland and Polish universities. They typically takes less time to take, for a few reasons (the number of questions, the speed of writing versus oral production of answers, the ability of the professor to ask probing and follow-up questions instead of having to give the same battery of questions to each student in a blind and generic manner, even when it is clear that the student has answered the question in another answer or another way). The goal is for the professor to establish with confidence the degree to which the student understands the material.
Now, yes, it takes more time for the professor to administer the exam than it would take to administer a written exam, but note that grading exams is also very time consuming. You can delegate to grad students, but the same can be said of oral exams, so there's little differentiation there. The oral exam combines the administration of the exam with the grading, whereas written exams separate the two.