I believe text areas where you write Markdown, such as in this very issue tracker, should use a monospace (fixed-width) font. This makes it easier to align stuff in code blocks and ASCII art diagrams and such. As a bonus, monospace also makes it easier to position the text cursor precisely using the mouse.
I can't find any scientific literature suggesting that monospace for text editing is objectively better (or worse), but I did take a brief look at what everyone else is doing.
First off, nearly all of us coders will be using a monospace font in our code editors.
StackOverflow, whose core business is having people write Markdown, and which strikes me as a pretty data-driven company, uses monospace (to be precise: Consolas,Menlo,Monaco,Lucida Console,Liberation Mono,DejaVu Sans Mono,Bitstream Vera Sans Mono,Courier New,monospace,sans-serif).
GitLab also uses monospace ("Menlo", "DejaVu Sans Mono", "Liberation Mono", "Consolas", "Ubuntu Mono", "Courier New", "andale mono", "lucida console", monospace).
GitHub does not use monospace. Rather than taking that as an example, I would see it as an opportunity where Bitbucket can do better