As someone who indexes a growing amount of org-mode notes (I like to keep as much within DevonThink as possible!), I heartily vote for this feature.
Point (with an eye to future implementation): Github already does this (see https://github.com/github/markup/issues/186), and Hugo (a popular static website generator) has a plugin for it (see https://github.com/kaushalmodi/ox-hugo)
Counterpoint: As pointed out though, it is not a trivial task at all, there are … numerous edge cases in rendering Org generally, and it might not be worth implementing this until “document markdown apps” (iAWriter, Marked, etc.) embrace rendering org-mode.
Also, since OP missed “linkifying” the related posts, and I can’t edit posts, mentioning them here: