This is shocking. This is a lack of basic literacy. Obviously MathJax is needed in chat.
The current situation with MathJax in chat is pretty annoying. Many users are using user scripts or bookmarklets to render MathJax in chat, which certainly works for them, but essentially makes the messages unreadable for anyone else without the script.
The existence of the user scripts and the heavy use e.g. the Math room makes of them do demonstrate the clear need for MathJax support in chat.
This is how the Math chat room often looks to new visitors:
It is certainly not a good user experience to see just raw MathJax source code if you don't have the user script installed. And user scripts don't necessarily work for all users or all devices, they are not a good solution.
Performance is usually a major consideration when adding MathJax, but I don't think this is an issue here. All the users that add the user script already experience the performance impact, and if it is only enabled on rooms that actually require it there wouldn't be any impact on users that don't really need it.
Chat rooms should probably just inherit the MathJax setting from their parent site, if it is useful on the main site, it is likely useful in chat as well. An alternative would be to selectively enable it for rooms that heavily use it now.