With so much note taking apps nowadays, I can't understand why does anyone still write notes with pen and paper. You need to bring the notepad, book or that paper to retrieve that information, and most of the time you don't have it in hand. While my phone almost always reachable and you carry when you go out. For those still like to do handwriting, there's many app does that and they can even convert it to text notes.
So, if you still write notes with pen and paper, why?
Typing is better than writing in a solid 75% of cases in my opinion. I agree that you tend to remember things that you physically wrote down better than things you type, but that can be mitigated against if you're in a situation where you need to remember things with strategies like spaced repetition.
In a lecture setting I would prefer to physically write things down, but you also have to be careful with this and only try and summarize because many people have the wrong strategy and try and transcribe slideshows or the lecturer's words verbatim, get halfway through a sentence, the lecturer moves on to the next page, you then have to try and remember the rest, probably get bits wrong, and by the time you've finished that then they're on to the next page and you're just not having a great time. If you get good at typing then you can keep up much better but that's still not the right thing to do in the lecture hall, unless your lecturer doesn't give out the notes or slideshows afterwards or record the lectures. then you're just kinda shit outta luck.
In just everyday settings, like writing a shopping list, keeping reminders? probably on my phone or laptop.