If you pay for Youtube Premium you can download any video to your device for offline viewing. I'm not sure if this is configurable by the video uploader. The video can still only be viewed from within the Youtube app so it's not like a general-purpose mp4. I suspect this is in part so that Youtube can continue to monitor how many times you watched a video so they can correctly compensate the uploader (and, obviously, to maintain control over their library).
How does YouTube operate the service with this feature? If enough people use it to download all the videos they want and then play them back without ads, then they're just hosting and delivering video for free. It's no secret that YouTube is already subsidized by ad-supported views and premium subscribers.
And YouTube Premium already offers a Download button. It downloads it in the exact same format as they send it to your device in - m3u8 parts.