My understanding was that its purpose was about notation/writing speed, in an age before typewriters/keyboards.

To use an analogy, it’s the morse code of writing, something that’s not really needed today.

I understand that perspective, no doubt typewriters and keyboards are a fantastic technology. Not that this really needs to be said but I don't want to make it seem like I am just shaking my fist angrily at the future.

However, the pen/pencil and paper is an extremely powerful technology and in many senses the rise of typewriters, keyboards and computers in general has made it more clear precisely what is so powerful about the technology.

It is a reasonable approximation to think of the process of handwriting as thinking of words you want to write and then just writing them out. The reality though is the physical motor task of handwriting feedbacks back into the cognition and impacts your thinking and memory retention. The specifics of that are complex on the neuroscience side, but we don't really to go deep down into the science. All you need to really understand is that the medium that we record and process information has an effect upon how our brain processes that information. Different connections are made, different things are obvious, different mistakes and discoveries are made.

One straightforward example is for many people when they are experiencing intense emotions or a difficult decision, the process of simply writing down how they feel can have a surprisingly significant impact on helping process those emotions. It isn't the notes the person makes at the end that matter, it is something about the process of handwriting (independent of metrics like how quickly information can be recorded) that does something that typing the same thing out on a computer doesn't do as well. Try it.

A more abstract advantage of pen and paper is that the process of idea generation can proceed extremely far before any explicit context needs to be defined for the idea. On a computer before you begin a project or try to flesh out an idea you have to decide what digital format to put your notes in (a word document? plain text? spreadsheet? a notes app? google doc?), create a file somewhere and then decide how many files of that type you will have for that project, how you will organize them and other decisions that are necessary to contextualize the idea you are developing. Whatever file type and subsequent software you choose to type in sets certain strict limitations on how you can extrapolate and manipulate on what you write. It makes certain kinds of directions an idea can travel in much much more difficult. A pen and paper has strict limitations too, a limited amount of space, a limited capacity to erase and no fast way to search for specific information but these limitations don't frontload the need for careful categorization at the beginning of the process. What you begin to write on a piece of paper can become anything, it can radically transform from one type of idea or data into another in a natural fashion. Your brain can make creative connections, uncover insights and most importantly radically recontextualize information when using a pen and paper in a way that nothing except an eink tablet with a stylus or maybeee org mode in emacs can even hope to come close to.

I am super ADHD, I lose everything includes notes, so I try to type important things up in digital documents. However I take out a pen and paper (or my supernote) and handwrite out my ideas and thoughts all the time. For big projects or ideas after I have developed an idea enough to understand the best digital context for it I can just transfer it (that transfer "cost" of having to type it out just being another mental processing step in reality) into some kind of digital form after context and structure has become a lot easier to define. For small projects the idea can live its whole life on the paper and never need to be recorded, the benefit living in solely in my head.

In general I think we should think deeply about why we have such narrow definitions of "technology" and what unconscious biases are embedded in it ("technology" must be hardware with computer chips or touchscreens or advanced sensors).