I use Basic Authentication for a few web services running on a server of mine and that I'm the only user of. It saves me a lot of work. I set the user and password in a file on the server and let nginx deal with it.
[1] https://security.stackexchange.com/questions/192828/firefox-...
One downside is that in trivial implementation (/logout page returning 401), you'll end up with credential prompt where no credentials work, and this can be pretty confusing if someone leaves the compute in that state. I think it can be worked around with "expiration" URL parameter or a cookie, but this is somewhat finicky to setup.
Mostly I just close my browser, that clear everything in my setup.
Why browsers do not have better functionality built in for authentication is something that's always been a bit baffling...