One thing paper helps me with is free-form thought externalizing.
When you limit yourself to text, markdown, or sometimes even a digital pen/drawing app, I feel like it requires a bit of effort to use which allows ideas to slip from my mind.
With a pen/pencil and paper, I can write, draw, and connect about as fast as I can think. I can crumble the page and refine the idea over and over until something I like is there.