Mechanical timepieces are a luxury item, and these students are essentially artists in training. Wrist time was solved in the late 1970's with the commoditization of quartz movements. These 'jobs' will get replaced by AI at approximately the same pace as your local sculptor.
I don't know if watchmaking is one of them, but there are a bunch of traditional crafts which are actually approaching a danger point because there aren't enough up-and-coming acolytes in the discipline to replace them, even though the craft still enjoys enough popular support to have a thriving economy.
Anecdotally, I see enough mechanical watches on wrists and in duty-free shops that I imagine there's enough of a pipeline there for at least one school. Much like vinyl records it doesn't appear to actually be going away even if it's superfluous.
Good example of that is engraving:
https://www.youtube.com/watch?v=yH3MtWln2Og
(ages ago, I was in touch with a person who described himself as "the last hand engraver in New York City" when considering an apprenticeship --- couldn't commit to the move --- always wondered if he found a successor)
Come to think of it, it makes sense; in this day and age, every industry is evolving so rapidly that the future remains quite uncertain.