I’m pretty sure I tried that at some point (in the past) and it had its own issues. One of them being that if you click on the video it takes you to the twitch website. That’s a big no no.
This is a desktop application where every stream (you can watch mutliple streams) is opened in a separate window (hence the use of /:channel/popout), so every window acts like a media player. Imagine a media player that when clicked takes you to some webpage.
This is also used in a desktop dashboard, where the streamer can view his/her own stream. Same thing, clicking the stream should not navigate away from the video player. That’s just bad.
Unless this behavior can be disabled - or changed to the default behavior where it goes fullscreen - the Player API is not an option.