Something they should have done long back, I had to use other Youtube apps just to listen to music in backgroud
The app looks beautiful and obviously they took a lot of effort to build it but this small detail makes it completely unusable unfortunately.
I understand that they are trying to sell Youtube Red this way but there's probably a better way than sabotaging their own app.
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.
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.