You have a link to that deliberate design decision? "Probably"? Sounds like you're guessing.
Even if true it looks bad. They spent 3 billion on an app and got all these music and TV deals and then they can't add an Airplay button?
You keep saying that, but, they didn't pay 3B just for an app. They also got a headphone business that made over 1B in profits last year and commands 60% market share for headphones over $100.