Universities already have systems in place to allow students with disabilities to take alternate forms of assessments. So, perhaps, students who can't deal with oral exams can choose to give written exams.
Btw, I was a professor and I saw students on both ends of the spectrum. Students who would bomb an oral evaluation because of anxiety but would do well in written exams. And student who would bomb written exams, but would totally ace an oral evaluation. Since, a professor's job is to create well-rounded individuals, courses should include a mix of different assessment types, so students slowly build up the skills to handle all of them. Of course, augmented by guidance and feedback on how they can build those skills.
Btw, I was a professor and I saw students on both ends of the spectrum. Students who would bomb an oral evaluation because of anxiety but would do well in written exams. And student who would bomb written exams, but would totally ace an oral evaluation. Since, a professor's job is to create well-rounded individuals, courses should include a mix of different assessment types, so students slowly build up the skills to handle all of them. Of course, augmented by guidance and feedback on how they can build those skills.