For some reason these services do not seem to want people to download anything to a Mac, perhaps this is because they offer apps for mobile devices and therefore have control over how those recordings are stored and how long they are available for (YouTube Premium only lets subscribers download video and music on to mobile devices, and it will only be available to watch offline for 30 days, for example).
The same is true of Disney, Netflix and Prime, who also allow downloads to mobile devices, but not the Mac. The most curious thing about this particular issue is that YouTube allows YouTube videos to be downloaded to an iPad or iPhone (if you subscribe to YouTube Premium, $11.99/£11.99 a month, one-month free trial). Making a copy of YouTube videos on an iPad or iPhone is really easy, but the same can’t be said if you want to save YouTube videos on your Mac. You can download those YouTube videos your kids (or you) love to watch to play back offline. If the idea of a long car journey or bedtime without a connection to the internet leaves you trembling with fear, there’s a solution.