A few months ago I developed and designed a chat service. This was something I put a decent amount of thought in, and the result just ended up being that I felt having the defined left and right meant that it was a lot easier to navigate.
The clear definitions between who is sending what makes the users life a lot easier.
Another aspect is that it depends on what platform you're targeting. Slack and discord for instance were designed for monitor screens, so having left and right makes it really confusing to follow. Messenger or iMessage were designed for mobile screens and it just makes most sense having the clear definitions.
I hope that's useful. Think about the platform you're designing for and what your demographic is most used to. Another thing to think about is do you expect multiple people to be in the same chat?