It makes it much easier to tell that you're writing or editing a post, for one, instead of looking at a completed post.
In addition, it's rather standard practice to have your font be monospace when composing a post if you're not using rich text. Since we're using Markdown, it makes sense to go with what's generally done and use monospace while composing. (See, for instance, the difference between using Wikipedia's visual editor and the WikiText editor.) This makes it clear that what you're typing is sort of like code - it's not what's literally going to show up in your post; it's going to be transformed in some way (such as asterisks making things bold or whatever).
If we were to add a rich text editor as well, then I'd be in favor of using the regular font there as well.