Ah really? I'm on Android and don't have a Youtube account at all. I mean the app should work the same way as desktop, the video does not stop when I switch tabs on my browser...
I understand that they are trying to sell Youtube Red this way but there's probably a better way than sabotaging their own app.
I think the reality of why they do this is to stop people using YouTube as a free music player, which unfortunately is a very common usage.
It's a shame this restricts other youtube videos too though, such as creators / original content / etc. I'd really also love to use Picture-in-Picture on iOS.
I can definitely see their reasoning, but like you, I don't like it. There's times where I really just want to listen to something and not need the video without it being music.
As for the Picture-in-Picture, there is a somewhat hacky solution. If you go to the video in Safari and install Pipifier (https://itunes.apple.com/us/app/pipifier-pip-for-every-web-v...) you can use it to start Picture-in-Picture. I don't use it that often due to the extra steps involved, but it does work.
On Android there is a better YouTube client available called NewPipe. It's FOSS and you can get it on F-Droid. It enables you to play music in the background along with other features.
I understand that they are trying to sell Youtube Red this way but there's probably a better way than sabotaging their own app.