David can listen to his podcast app in the background, but YouTube TV shuts off when he's doing something else. What gives? Leo says that once iOS14 comes out, the picture in picture will be activated (it already has on the iPad). Apple has been very careful with what runs in the background and Apple is very aggressive in killing background processes. But YouTubeTV will be one of those that will PiP in the fall. David could try the Public Beta right now by signing up for it here. But it's up to YouTube to enable it, and they may not have with Youtube TV.
It may work on a browser though, per Carmine in the chatroom. Run YouTube in Safari.