That's a very common misconception of private copy; the existence of the private copy tax is not excusing copyright violation.
What private copy wanted to cover is more like "I bought a physical CD and I make a cassette copy because my car doesn't have a CD player" or because I want to listen to a mix of my favorite music (so you paid a tax on cassettes and later on CD-R and CD-RW media). This was later extended to "I copy all my collection of music to a hard drive and stop flipping CDs in and out of the player" (so you pay a tax on hard disk drives).
It seems kind of the same to me if the result isn't being distributed again: "I want to view this YouTube video on the airplane when I don't have internet access." (Let's assume no international travel is involved to avoid questions of regional licensing rights.)
YouTube's paid offering in some countries includes this feature on Android and iOS, but for computer users there's no built-in way to do it. Wouldn't it fall within the spirit of the private copying rule for a subscriber to YouTube's paid service to use youtube-dl in this way?
> That's a very common misconception of private copy; the existence of the private copy tax is not excusing copyright violation.
You are wrongly assuming that a copyright violation has taken place. If a country's laws say it's legal to make a copy under specific circumstances, it's not a copyright violation to make a copy under those circumstances.
What private copy wanted to cover is more like "I bought a physical CD and I make a cassette copy because my car doesn't have a CD player" or because I want to listen to a mix of my favorite music (so you paid a tax on cassettes and later on CD-R and CD-RW media). This was later extended to "I copy all my collection of music to a hard drive and stop flipping CDs in and out of the player" (so you pay a tax on hard disk drives).