This is such a silly idea.
It’s a chat room that works more like real life (I highly recommend real life). It only shows the last thing someone said. That way, if you want to follow what’s happening, you need to pay attention, which is important, I think. It’s a synchronous chat app. No async messaging is possible, really.
It also uses color as the only way to distinguish people, so there isn’t some mostly-ignorable-but-important identity component, username registration, or anything like that. Just like normal conversation, you’re looking directly at their identity. You can, of course, introduce yourself.
There are different rooms. You can send people links to rooms.