Questions without $\LaTeX$ are pretty annoying and, even though the users might get motivated by seeing questions with it, shouldn't the site be more active encouraging its use?
Is this a real problem? If it is, could a badge solve it?
First of all, several questions do not require $\LaTeX$. I do not have a statistic on how many questions require $\LaTeX$ but I know that there are quite a few which are simply text, although, agreeably this is slightly rare.
Second, a badge would not resolve the issue much. You can teach a $\LaTeX$ dog new tricks, but not when they are interesting only in getting an answer to their question. If they do not know $\LaTeX$ and are desperate, they will post in whatever formatting they can and not care about how readable their question is. Usually, people who care about making their posts understandable and convenient to read are those who care about getting badges $-$ this is not a strict correlation but, IMHO, this is pretty accurate. Therefore, I think adding a badge (especially since it would be bronze) wouldn't change things much.
Next, how would you even implement such a badge? What is the requirement to earn this badge and where would it be valid? Just Math.SE and MathOverflow? Doesn't seem logistically trivial.
Finally, I don't think the admins are interested in making a change to the badges system right now, and anyhow, what's the whole point of those who edit posts? There is an entire section called review and multiple badges to reward those who spend time making these edits. So there are several people already making edits pretty quickly. There's not too much to be annoyed about.