This is already the case for Master's degrees and above in Denmark. I've been the opponent examining students. We ask Master's students to give US instruction on a topic (drawn randomly on a card in front of them, from a list they know a few days in advance). They do a chalk and talk on a topic for about fifteen minutes with three to five professors being "dumb students". It works fantastically and at the end it's ve…
Hi, former student with social phobia and terrified of public speaking. Today: adult with no problems doing public speaking in front of hundreds. What fixed me: more public speaking and not having the option of avoiding the task.
What also helped me is being so knowledgeable about the topic that I didn't need to prepare the presentation much (except for the slides and the general plan). When you know what you have to talk about, it becomes a lot more natural and relaxed for me.
I would be a lot more stressed if I had to learn a presentation by heart and it would probably be a robotic delivery.
So I did quite a few "surprise" presentations, with very light prepared material and a topic I cared about. Got me the practice I needed and I learned not to get "stuck" as if I forgot the next sentence. The presentation always flows!
Now, I have a talk at a major conference, and I'm afraid this won't work there, so I'll prepare my talk better this time, maybe even have speaker notes!