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?
Because you remember it better when you actually write it out instead of just using a keyboard. And you can draw diagrams with ease. Most styluses are inaccurate and one dimensional, and buying a phone with actual proper stylus support in both the display and stylus itself is expensive. You could buy a separate technical device just for note taking with proper stylus support and have it upload notes to the cloud so you can access it at all times, but that requires a constant internet connection and mobile data is expensive. And then you have to carry this seperate device with you in the same way you'd carry a much cheaper physical notepad anyways.