There are workarounds. One is using a free iOS file manager app like Documents by Readdle. Use the Safari browser to visit a YouTube video, and use the Share option to find Copy Link. Then go back to Documents, and use the built-in browser in the app to surf to a video download helper site like SaveFrom.net. Paste the link into the form (hold your finger down on it until you get "Paste" menu to pop up). The site will give you the links to download, and you can save the file to Documents. Hold down and drag the file up, until you're back on the main screen, then drag it to the Photos folder. You'll need to give Documents permission to access Photos the first time. You can then access the video like you would any video taken on the phone or tablet—in the Photos app.
If you’re looking to download a whole YouTube channel at one time, this is definitely one way that you can do it. WinX YouTube Downloader can download over 1000 URLs. Even more, it has support for different YouTube playlists and channels and even gives you the ability to record your own live videos, so this is one platform that can definitely achieve a whole lot more than you might have thought. On top of that, it doesn’t give you any kind of ads (because who wants to watch those?) and it lets you download from just about any kind of platform and into just about any kind of file.
The web browser Safari can be served as a Safari YouTube downloader, which offers an easy way to download any HD 720P/1080P videos on YouTube as well as other web. And for a successful YouTube videos download on Mac OS X, please make sure you have the latest version of Safari. Follow the detailed guides and learn how to download YouTube videos on Mac using Safari.

The Chrome Web Store—where you get Chrome browser extensions—is controlled by YouTube's owner Alphabet/Google. Even an extension ostensibly for this purpose—like the obviously named Video Downloader professional above—states right up front in its description, "The download of YouTube videos to hard drive is locked because of restrictions of the Chrome Store." In general with Chrome extensions, the download of any RTMP protocol video (protected videos) or streaming video isn't possible.

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