Q:

What should we do about broken Tex math markup in postings?

What should be done about postings that contain embedded  math markup in them?  
Certainly we should not ask for that to be enabled; its cost is much too high!
Should we replace them with images with the markup evaluated so that the text can finally be read?  To show how nasty it looks, here are example postings with this problem: 1, 2, 3, 4, 5. So instead of this sort of garbage:

The square root of the matrix $A$, denoted by $\sqrt{A}$, is well-defined.

It could be replaced with this image:

Sometimes this can be done with Unicode so that it can be left as text, but unfortunately, Georgia is not well disposed towards the needed combining characters.  For example:

The square root of the matrix , denoted by √̅, is well-deﬁned.

At least on my computer, it does not correctly join up the overline to the radical sign, and so is inferior to the image replacement.  
However, image replacement is a pain to make look good — I have not tried to do so here. I just think these math-markup bits look ridiculous, and that we should do something to improve them.
I’m not quite sure what, though.

A:

Enabling MathJax
As a moderator on Code Review who helped to push for MathJax to be activated there, I can say that the current Stack Exchange policy makes you work hard to justify it.  Performance is a Feature, and Speed Still Matters, says Jeff Atwood, so they want pages to render quickly.  MathJax is enabled per site, not per question, so they are reluctant to incur the performance overhead of loading and executing the MathJax code if it is deemed non-essential to the site.
To request MathJax to be activated, the community needs to come up with a list of posts that would have benefitted "extensively" from MathJax.  That is a tough request to fulfill for EL&U.  (Code Review had to work hard to convince SE, and we sometimes deal extensively with mathematical notation.)
Making do without MathJax
For the most part, it is possible to convey basic mathematical notation with a combination of Unicode, ASCII art, and, as a last resort, images.  One way to make an image is to use latex2png.
Specific posts
I've gone ahead and typeset the specific posts mentioned here using Unicode.

