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.
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If you want to download as videos itself, you can use other free tools like Free Youtube Download to download all videos with a single click. Please be careful while installing this tool as it optionally installs a browser toolbar and modifies search preferences. So please make sure you read and uncheck the optional checkboxes while installing to avoid surprises in your browser.
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.