I was the PhD student in the room in dozens of these exams, and I toke some of them myself. But that was for classes with a bit less than 40 to maybe 60-80 students. The load for the larger ones was shared among professors, if I remember correctly. But it was certainly the case that a single professor spent 1-2 days doing nothing else but these exams.
And it was 1 professor and 1 PhD students, and those don't count. They essentially grow on trees and are always available, if you need some.
Since each course needs its eval, assessment is a function of N, not N*K or K. Much easier to scale if there is ~5 evals per student per year than ~20.
I think education is something better scaled horizontally than vertically. More schools, with more professors instead increasing the student per professor throughput. The classes where I learned the absolute most, and had the best experience, were closer in size to 25 than 100.
With an oral exam, the prof blocks off 3 days or so, with ~8 students per day and it's done. It's not a huge additional effort compared to all the effort of giving the course over the full semester anyway.
An added, though minor benefit is that the professor might decide to offer a student assistant job to someone who performs well, because it's much easier to judge who is actually good in an oral exam vs in written. There's a reason that job interviews aren't just tests filled out on paper but involve personal interactions.