I, on the contrary, think Apple Music is run at loss with the express goal of getting all other services out of the market. I simply don't see why Spotify would be operating at huge loss and Apple Music with all its exclusives (they don't come for free) wouldn't. Apple can afford to put a billion dollars into AM. Tidal, Spotify, Deezer etc. don't have that possibility.
Spotify has 100 million users... but only 30 million users pay for it. And the ads on the free tier don't even come close to covering their costs. That's why they operate at a loss. And they're still acting like a startup accepting billions in venture capital with no signs of becoming profitable even after 8 years.
Sure... it's possible that Apple Music operates at a loss... but it seems unlikely since they don't have a free tier dragging them down like Spotify. Every one of Apple Music's users pays to use the service... there are no freeloaders.
The only question is how much does it cost for them to run Apple Music compared to the money that is coming in. I would imagine they designed it to be profitable from the beginning.
As for Apple trying to get the other services out of the market... Spotify wasn't profitable before Apple Music... and they aren't profitable after Apple Music either.
They were in trouble before Apple even entered this market.
Another theory... perhaps ALL music streaming services lose money. Spotify, Apple Music, Google Music, Amazon Prime Music, Microsoft Groove Music, Tidal, Deezer, Pandora, etc.
But only the major players like Apple, Google, Amazon and Microsoft can afford to lose money just to please their customers.
That's another possibility.
But I honestly don't think Apple would do anything to lose money on purpose. I could be wrong though.