It seems like it must have something to do with different departments tracking revenue, but the way this is being rolled out is pretty strange. There's no mention of it anywhere on the YouTube homepage, so you would have to search for it specifically, and it's not even the top result on Google when you search for "youtube red." To know that you have access to Google Play Music, you have to scroll all the way down to FAQ point 5. Maybe the subscriptions were integrated recently and the administrative barriers to approve new marketing materials prevented them from being ready for launch. But I can only speculate.

I think with this initial pool of already signed-up users, Red effectively skips the first stage of user attraction.

I am not familiar how accounting works for this, but Red would have a pool of revenue to distribute to from very early on, so the creators would have more incentive to create Red-exclusive content. Nice bootstrap strategy indeed.

Maybe. It's also a pretty fair acknowledgement that Youtube Red is bundling Google Play Music in for the exact same price so "Why should people with Google Play Music have to cancel their subscription to GPM and sign up again for Youtube Red?". Instead just give it to them as part of their current subscription.