I.e., I would actually love to have a list of the videos I've watched recently - on my device, with a simple option to delete it, exactly the same way that browser histories have worked since forever.
However, with YouTube, it's all or nothing: Either, I let them track my viewing history globally across all devices, store it on their servers for all eternity and do who knows what with the data - or I don't get any history at all, to the point where when I restart the app, it will completely forget the video I just watched a second ago.