We want the most basic (in the sense of "fundamental") functionality of the Stack Exchange sites, asking and answering, to work without JavaScript. Most advanced stuff like voting, flagging, UI niceties, help texts, favoriting, global inbox, and whatnot require JavaScript, and that's okay. But the one thing that the sites cannot live without – Q&A – should not have that requirement, to keep friction as low as possible.
Of course, when you don't have JavaScript as a requirement, you can't require that the client render the Markdown.
Even if you re-sanitize on the server-side, allowing the client to do the rendering obviously removes the trust that you can have in the rendered version really being made from the Markdown. Imagine the following:
I, an evil spammer, post the following answer:
As you can sea on [this awesome site][1],
... (long text on thread-safe usage of the turtle in LOGO) ...
Hope that helps!
[1]: http://almost-real-rolex-watches.biz
But I submit a rendered version in which the link actually goes to a relevant site on the intricacies of turtle concurrency. Since the server expects both the Markdown source and the rendered HTML from me, it trusts that the one was made from the other.
Along comes Sean Sceat, renowned Stack Overflow user with 120k reputation in the logo tag alone. He sees that the link indeed goes to a relevant page, likes the answer, upvotes it, posts a "Great answer; the site you link to has tons of helpful content!" comment, and while he's at it, he fixes the typo "sea" -> "see" (which the spammer made deliberately).
But the Markdown that was in the editor after he clicked "edit" did not contain the relevant link anymore; it contained the Rolex link. And thus – unbeknownst to Sean – he not only fixed the typo, but also changed the link to go to the spammer's site.
Now you have a post with the last edit coming from a trusted user, endorsing the answer, but with a link that we'd rather not have people clicking.
And the revision history (see point 2.), would not even show that the link was changed.