PHP and cocaine.

In the past Latex symbols were rendered on server as an image.

It was not pretty but it works virtually anywhere.

What part of a Mathematics Stack Exchange clone would require JS?

In "modern" stacks it is preferable to do things like layouting of formulas millions of times on the clients, instead of once on the server. I guess that sort of thing needs JS.

As you have pointed out, but formulated more explicitly: client-side rendering should deal only with HTML/CSS because that's what the browser is built and optimized for. Every line of script changing the DOM (html structure) may trigger a redraw of the page, which means wasting considerable amount of resources! But even if your script outputs HTML only once, you still have O(n) HTML templating instead of O(1) for n clients. Such a waste!

The MathJax part.

MathJax is somewhat convenient but doesn't seem necessary at all.