Even on paper I write in a bastardised, paper-friendly subset of Markdown. I write underscores to denote words I wish to emphasise, a greater than symbol to indicate text I am quoting, and surrounds words that will later form a link with square brackets.
I suppose it shows that the primary intent is for what I write to be put on the web. In that regard it is helpful but it also means that I'm thinking about formatting, about publishing, rather than just on the word themselves. It definitely shows that I am used to writing for the web and only now transitioning back to paper as though it is some strange concept.
This creates a conflict between getting the words down and ensuring those words will be presented in the way I originally intended. It's a conflict between flow and refinement, when the writing and editing should be separate, distinct phases in the process.
Maybe I'm just overthinking it. Maybe I should just stick to what works for me, what seems to work at least.