Taking notes forces your brain to process the information in a way that just reading or listening doesn’t.

You only have one language processing centre. You are either copying from the screen or listening to the professor, not both.

This is definitely how my brain works. I'm either absorbing words that are said, or I'm writing - when I multitask here, my retention plummets like a rock.

Shocker, that. Multitasking worsening performance? Surely that can't be a super-well-demonstrated-repeatedly phenomenon.

It also means instead of listening youre busy writing down stuff in time before the next slide

That isn't a justification; if the students think that it helps they can take notes of their own initiative; handing out a copy of the slides doesn't disadvantage anyone. The lecturers are just making a petty power play because they want to feel important standing in front of a bunch of eager young students

There simply isn't any pedagogical justification for withholding information post-lecture that was deemed important enough to be included in a lecture. Everyone knows this material is critical to understanding the course. If professors want simple optimisations to help students learn then they would be doing something like organising lecture material to promote spaced repetition.

except you don't have time to do that in the moment, since you're busy scribbling down formulas trying to keep up

Does it? I once had a course where for some reason administration cut the course hours in half, without cutting the program. Teacher apologized in advance and asked us to take notes and read them at home later. After every lecture, I kid you not, I was lucky if I could remember the topic that was read to us. Absolutely no facts. It was lectures on topics I was slightly familiar with. And the speed of the lecture wasn't even as high (sic!) as the speed of some youtube lectures I have watched later.

You need to have time to process, but when you have to take notes there is a speed at which you just skip processing and instead all of your focus is in transcribing as efficiently as you can. I imagine, the speed differs from person to person. For the most of this course, the teacher hit this speed. And she knew she would hit it. So it seems universal.

If current student generation is worse at taking notes by hand, it could be a real disadvantage for them

I learned better when I took notes. I believe research backs that up.

Probably an obvious addendum here, but the classes I remember having the most engaging lectures were flipped style where you didn't need to take notes necessarily, because the class was about discussing and deepening the understanding of material you saw already. That was true for my physics classes as well as philosophy. I think it was doubled up in usefulness when we were assigned material that asked us to act on our deepened understanding soon, e.g. before the next class period, such as one of the many "opinion pieces" we wrote for things like dualism/monism, etc.

Technical subjects achieve this with labs, too. It doesn't scale but we see clearly that scaling isn't always very desirable, especially if it leads to this regression.