yt-dl.
You can also watch it in a proper player that gives you more control over playback than what the JS from google gives you.
You can watch it anytime, anywhere, even when you are somewhere without an internet connection.
You can watch it on any device capable of playing the content, whether or not those devices can access youtube directly and/or can stream from youtube.
You can transcode it for playback on another device that is unable to play the original file.
You can watch as much as you like, pause, take breaks, jump backwards, forwards, go into slow-motion, do frame steps, all without google recording your every interaction with the video.
As with downloading music: that's exactly my question. Why would people download and play music like 10 years ago while there are numerous streaming services out there?