YouTube premium lets you “download” videos but I don’t think it doesn’t actually let you get an MP4 file. It just lets you watch the video offline.
But normal YouTube videos aren’t DRMed at all so you should be able to find the file in cleartext somewhere on your hdd
I don’t think you can use that feature on the web. It’s mobile app only. Maybe you can use adb to grab them off an android device but it’s not nearly as easy as youtube-dl. I wouldn’t be surprised if they were DRM’d in that scenario anyway.
If, for some reason, I really wanted to download a video to have a copy of it forever, I'd use youtube-dl