In my university, in Italy, most professors want students (at least the undergraduate ones) to handwrite what they are saying in an oral exam. If I understood correctly, this is somewhat due to needing an official document for the oral exam. Does this occur in other countries too?
It's not uncommon for students to have a not so clear handwriting (I know many), one has to put care for the text to be clear, it ends up being kind of distracting. Maybe that's not to the point of being a huge problem, but nowadays LaTeX is anyway an important instrument for a mathematician, would it not be feasible to offer a LaTeX course in the first semester of the first undergraduate year, and then have LaTeX-assisted orals? I think the speed of handwriting can be partially undermined by the need to put that (probably extra) care, resulting, in average, comparable to the speed of LaTeX-typing after an entire dedicated course. Is there a good reason not to give the students a keyboard and a monitor, provided that they have been taught LaTeX? In the end, the printed document would be manually signed.
(Added stuff from the comments)