I find another benefit of blackboard presentation is the order of information. The lecturer can build something up rather than simply showing the finished article and saying voila.
Working a project on a blackboard also encourages people to get the order right. It's surprisingly common to see Powerpoints which skip or reorder steps completely because the slide creator shuffled things around or worked backwards from the answer.
I'm sure most people have seen professors skip numerous steps on blackboards, too, but in my experience there's at least a heightened awareness of what it looks like to actually work through the problem.
What's best about black/whiteboards for me is precisely the nonlinearity. Numerous times I've seen professors realize near step 10 of the proof that something they said in step 3 isn't quite right; then a sidebar is opened and arrows start to be drawn to piece the puzzle together.
The point of going to classes versus studying alone at home is that you get to watch mathematicians doing mathematics. It's apprenticeship learning, the same as carpentry. Watching the professor reason and make mistakes and second-guess himself is invaluable. The typed class notes where everything is neat and theorems are numbered gives the impression of an immaculate birth that the student can't fathom arriving at. The best maths classes are the ones that teach you how to be a mathematician.
This is a much better expression of what's great about chalkboards than just the order of steps, thank you. It's not so much seeing a problem worked out in sequence as seeing it worked out for real. Even if the professor is working from lecture notes with all the steps, writing them out live engages with the content in a way that pressing "next bullet" doesn't. And as you said, what's missing is the messiness - catching mistakes in the notes, making mistakes on the board and finding them, puzzling over what belonged at a missing step.
Everyone jokes about the frustration of copying a full blackboard worth of notes and then having the professor go "wait no, that wasn't right" (myself included) but it's a valuable experience. That moment of "hm, hold on a second" is where the math is happening, and a chalkboard helps professors and students notice that. (And of course, when something "isn't quite right" on the Powerpoint, it's a tremendous pain to fix...)
A great teacher will be a great teacher with whatever you give them. But anyone not 100% tuned to that part of their teaching greatly benefits from some of the constraints that chalk gives them.
I'm a K-12 admin and once we had a HS teacher who was brilliant but her classes were often too difficult to follow for the kids. We just told her she couldn't use the powerpoint slides anymore. Yes, there was a huge discussion of timing and pedagogy and all of that, but ultimately, placing that constraint on her naturally put her at a much more equal footing to the students she was trying to teach.
When you try to force could behavior by handciapping people, you also get utter failures like teachers with bad (or too-slow) handwriting who cannot succeed at conveying information via the arbitrary restriction.
I think it's even better if the slides are posted prior to the lecture so that interested students can make their notes annotations on the slides - this allows them to fill in trouble spots while not having to copy down all the material (I find it distracting to try to rush to copy everything down, personally).
As someone in college who has had their classes recorded and posted online, I still go to class because its dedicated time to my brain. There is nothing else I should be doing other than being in class.
The people who don't show up would have not showed up class recorded or not. It is very useful though when you have a morning class miss or be dead tired and not pay attention to re-watch the lecture to get a better understanding.
It seems like whatever recording either I or the professor make are actually useful to me later on. It's always the classes I don't record are the ones I always need.
If no one goes to the physical classroom why not sell the same recorded lecture to a thousand people online instead of the 100 that fit into a classroom?
I had a world history/geography/current events kind of class in college that had an in-person lecture and was also livestreamed and recorded. Lecture hall fit about 1800 people but he also had an unlimited class size "online" section you could sign up for if you didn't get in-person section during early course request. You never actually had to go to class. The professor had to get his own system for taking quizes and handing in assignments since the online learning management system the school used would choke with that many students at once trying to submit things.
Content aside, it was a very interestingly run course. Assignments were at your own pace, you had a large list of the kinds of projects you could turn in for credit. There were quizzes, exams, essay topics, interview topics, and an option for independent projects to get credit. Each kind of project had it's own maximum point value it would be graded out of and the final grade was totally based on how many points your actually earned, not out of how many. Even if you did a shit job on every assignment, as long as you did enough of them, you could get an A. It was a nice way to boost the GPA from just sheer effort rather than actual achievement.
I'm sure most people have seen professors skip numerous steps on blackboards, too, but in my experience there's at least a heightened awareness of what it looks like to actually work through the problem.