I'd argue that Youtube is a strong video discovery mechanism and "People don't really choose where to watch videos" is very much false. Many people watch videos by directly searching for them on youtube and by subscribing to specific "youtubers" (perhaps it's different between various ages/demographics, though); and, IMHO this is the largest part, when watching the next video people stay on the same site, at least in the case of youtube; they'll just pick one of the recommendations and it's not going to be on another site.
We are basically making the same point. People don't watch the videos because they're on YouTube, people watch the videos because the app on their phone only plays and searches videos on YouTube.