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 ;)