Or if you want to play something without video at all for e.g. music livestreams, that can be done too. Example below uses the famous lofi girl stream.
Maybe that behavior is Linux-exclusive? Under macOS and Windows, if I only use --ytdl-format='bestaudio/best' with livestreams mpv will spawn a window with the video.
I'm on Windows as well. Just get rid of the 'best' argument for '--ytdl-format'. Also, 'bestaudio' is mostly only known as a keyword for Youtube videos.