You can be streaming while not listening though. I tend to leave my music streaming on after I leave the room because there is something quite enjoyable about walking inside and hearing music.
Remember all that promise of neurohacking in the near future that people like Ray Kurzweil liked to write about? One wonders if once techniques to boost the human brain’s bandwidth arise, they will be used in large part to allow people to consume multiple content streams at once. Imagine the boost it would give to a person’s erudition to be able to watch a classic film, read a classic novel, and listen to a classic recording all at the same time.
This is the main reason I'm skeptical that other forms of media are distracting from streaming. Someone could easily turn of Dota 2's music and listen to Spotify in the background.