One benefit of saving the rendered html along with markup in the database is that you can make breaking changes to the parser (like swap it out entirely) without worrying about old posts.
I specifically made keeping the original markdown text. The parser will improve. For instance, I plan to make a @mention and #hashtags. Like a twitter. With email notification when you mentioned.
A ready HTML stored in a database, to avoid wasting CPU time for parsing each time the page is viewed.