"Downloading" doesn't mean "saving a copy" (unless you count "saving a temporary copy of its chunks in RAM"...). Most of my youtube-dl usage comes from its mpv integration, so the video is simply streamed directly for playback.
It support a gigantic amount of website, including audio one. Most of the time, I use it to have an offline copy of a podcast, radio show or some video that I might need to look at wherever I am not guarantee to have an internet connexion (very useful when travelling).
It also has a lot of useful option like downloading the audio only of a video, choosing the quality of the video/audio which might be hidden in the website you are trying to watch it from, download subtitle (this is just so useful), you can pass ffmpeg options also to post-process the video in one go, ... There is just so many thing you can do with it. One last example : one of my computer really struggle to watch video/stream directly from the browser (for whatever reason), but with youtube-dl I can stream directly to VLC/MPV and it use 1/10 the CPU comparing to watching the same video in the browser.
youtube-dl is a networked multimedia swiss army knife supporting many operations and manipulations of audio, video, metadata, and auxiliary content from many video and audio hosting sites and platforms, as well as serving as an access layer for several playback tools, including mps-youtube, mpv, and VLC.