Chat rooms work very well for chatting. I'd consider myself a power user (#3 chattiest user on chat.se, and #2 is a bot. #1 probably has 3 times the heads?) and the fact that there's 'barely enough user interface' means things stay out of my way.
It's worth remembering
LaTex MathJax support is only active on a subset of sites, and markdown works for most sites/people. The chat servers for most sites (MSE and SO have their own) are shared. Even where something isn't directly supported, copy/paste is an option (and I've done that a few times with languages I can't type in, and emoji). It would need rich text controls, which many folk can do without (tho I suppose it could be toggled).
"Barely any user interface" kinda reflects the philosophy of SE as a whole - we don't really need a ton of noise, and the somewhat minimalist design works. It's basically a lot like the average IRC client with a few modern niceties. I even heavily use the even simpler mobile chat extensively in certain situations.
And as someone on... let's see, Slack and Matrix - the UI is oddly similar since there's not that many ways to do chat. Text box so you know where to chat, transcript so you know what's being typed. I suppose you can throw in rich text controls à la the main sites, but that just gets in the way after a while.
I'm not sure there's much to be done to chat. Sure you can polish it and make it pretty, but I'd rather have chat fast and simple, than some pretty, slow monstrosity that tries to tick off all the latest hipster features.