I have a very good opinion of your answer. You mentioned three ways how to think with a pen, I would like to explain my point of view for every of.
Stylus to a screen. It’s a good skill for digital illustrators, artists. Of course, a designer who works with and for Interior, fashion, games, industrial, jewelry or products absolutely need to draw for succeeding at work. And anybody, who works with graphics, knows what stylus is faster than a mouse.
Marker and whiteboard. It’s cool. The design process is about problem-solving. Thinking on the whiteboard is really helpfull in Design thinking, but there is no need to be a good artist. Is not necessary of beautiful lines and shapes. Because sometimes it’s impossible to change business process by sketches. For example, provide services in the branch of the bank. There a designer has to develop guidelines about a text, EDI, not just a fancy sketch. So, we should draw CJM on whiteboard, not illustration.
Pen on the paper. If we talk about UX: modern UX design it’s simple shape and text, and really, I don’t see there need to have good drawing skills. Yes, a designer must not draw ugliness, but the artistic view is more important.