If you are looking for a free online video downloader which supports downloading any video online from any site using URL, you definitely can not miss VidPaw Online Video Downloader. VidPaw is able to convert videos from YouTube, Vimeo, Instagram, Facebook and so on to many formats like MP4 in high quality. No software is needed and easy to use on both Windows and Mac.
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The next page will show a list of all Google products associated with your account whose data can be backed up. All of them will be selected by default, so make sure to unselect all and select only youtube. An easy way would be to untick the "Select All" button at the top which will unselect all items. Then scroll down and check the "YouTube" option.
When you copy a YouTube URL (even for a playlist), click in the WinX software to launch. You start with the "analyzer," which checks all the options. This tool also tried to default to the 1,920-by-1,080 version in MP4; I picked the 4K version (3,840 by 2,160 pixels) in WebM format, a subset of the MKV format—you can rename a .webm file to a .mkv and it'll work fine. In settings there are options to default to WebM at highest res. You can set up a number of videos to back up before you even click the download button. The 4K 575.4MB file took 1 minute and 39 seconds to download, more than double that of 4K Video Downloader.
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.