I would really like to watch my movies on a big screen via my Chromecast, but listen to the audio via headphones connected to my mobile phone. It is very handy if other people share the same room and you want to watch a movie, but don’t want to disturb them. Second, headphones sound very good and the movie becomes much more immersive.
If delay is a problem, then just make an option to manually adjust the delay of the audio, so the user can sync the audio with the screen.