Paper in my experience can get messy real quick. Example - When drawing a diagram of some process it is common for me to want to tweak and reconfigure things to arrive at a solution. With paper, it requires you either erase, scratch out, or re draw the diagram with your desired changes on another page.
What I love about marker boards is the ability to freely draft and modify on the fly without worry. When I want to commit ideas to "storage", paper works best :)
I agree 100%! Though I prefer to store things digitally. I feel so liberated no longer having so many scratch pieces of paper around that may contain an important note or solution to a problem. I remember working through a calculus book and having about half a foot's worth of paper (notes, attempts at solving problems, rewritten solutions to problems, etc) that eventually fell victim to entropy and was absolutely useless for anything but that I kept around out of fear of forgetting all of it. At least now it's all in one box. Maybe I'll burn it this winter as kindling - or would that be too derivative? :^)
These days, anything short term -> whiteboard, anything refined and meaningful enough for reusing later -> PC.