Do I do it? Yes. Should everyone do it? I hardly think so.
For a lot of people it is much easier to think and memorise things when we jot down stuff. There are a bunch of studies on the subject, so let's not get into this deeper. I tried some alternatives. Taking notes in Emacs was hard, especially because I work in Emacs, so having an extra window (a window is a panel-ish thing in Emacs lingo) was eating up too many screen estate. Doing it in another app was better, but I can't keep it on top forever, again, because of screen estate. Also, I really missed the fine movement of my hands. But the idea to give up on paper was strong, so I bought a drawing tablet (xournalwas an awesome app to use it with). I used it almost for a year, but the screen estate part still bothered me. I simply can't keep my notes on the top while writing the code. It also serves as a distraction, so at the end, computer based note taking had to go. I have a pencil and a bunch of papers next to my screen when I'm in the office.
On the other hand, I know a lot of people who hate writing. This is mainly because of bad childhood memories, as they were forced in a bad way to learn and exercise it. They use a note taking app or their phones to take notes. Some of them also use this opportunity to peek at their phone notifications, but let's not judge them.
Finally, it is worth noting that I don't write that much. I usually use pencil and paper during the planning phase, when having actual, working code is not necessary yet. Instead, I write and draw diagrams on how to do it. Then, I transform it to some primitive code, and start refactoring it. At the end, I don't use more than two sheets of paper in a week.