I don't log in. I use the stream key instead. So I don't have the other problems either, that people report about the login being funky. Just have a persistent stream set up on YouTube - no scheduling, just there - and start throwing data at it when I'm ready to go. Stop the data, and it times out, ends that stream, and resets to be ready for the next one. The stream information is entered on the website, not in OBS, and it's remembered on the website, not OBS.
The generic URL and that key are all that's needed, and both are included in the Profile. Change that, and you're streaming to somewhere else.
I'm only on YouTube, so I can only comment on that. Don't know if Twitch works the same way or not.