Really? That sounds like way too much hand-holding for a college course. I certainly had times when the teacher told us things that would definitely be on the test, but they didn’t do that for anywhere near the majority of the test content, only when rattling off a bunch of trivia and noting which of that was actually necessary to remember (i.e. remember start and end dates of WW2, but not the date of every battle).

Tests should be more about concepts rather than trivia, so “write this down” shouldn’t be a very common thing.

I’d agree processing and summarizing helps with learning, but that’s totally irrelevant and doesn’t have anything to do with writing,

But it’s not. Studies have shown that handwritten notes improve absorption of material. You can obviously get the same results by improving other study methods (i.e. reviewing and editing digital notes later), but if we’re strictly talking about note-taking itself (i.e. if you discard the notes afterward), handwritten notes are superior. So if you’re in a situation where you have audio (or better yet, transcribed) lectures, handwritten notes can improve your mastery of the content. You’ll get much more value from recording lectures and hand-writing notes during class than typing notes into a computer.