On iPhone the YouTube app will do full-screen in portrait mode. Grab the video title (under the video) with your finger and pull down. The rest of the UI goes away and you just get the video shown in the middle of the screen with large black areas above and below the screen.

This is besides your point but I thought I would mention it. I like controls that hide in full screen mode regardless of portrait or landscape because you want to focus on the content.

Not anymore, you can force portrait fullscreen In desktop for example: If you go into a vertical video with a regular "/watch?v=" URL, you can see vertical format video with regular controls

There was some way to get the same effect in android, but I can't recall right now