I think you understand it well. Its more of a bonus for Apple that they have half Spotify's market share really.That is a great question, however, how do you explain the early 2000s dominance if iTunes across both windows and MacOS? I know that iPods were a thing, so they wanted to make it so more people, who didn't own a Mac, could get one and upload music. I guess this isn't a simple question to answer. Are there windows users that have iPhones and could benefit from a better apple music experience? Sure, but I don't think apple necessarily cares anymore. I'm not Tim Cook, but I see apple music as an enhancement to the ecosystem and I honestly do not think their objective is to overtake Spotify, just to make sure Spotify doesn't dominate in THEIR personal market. I'm not saying its right. And I'm not trying to downplay the legitimate complaints of windows and android apple music users, but its very possibly they don't really care.
The prime objective for Apple historically has been to make sure that all its users have access to core services and software. In the past Apple has been at the mercy of Adobe, Microsoft etc.. in that it's Mac platform wasn't supported well. And there wasn't much they could do about it.
So Jobs started making Apple have these core programs like Logic, Aperture, Final Cut etc... And in the modern world it has Apple Music, Apple TV etc.. So you can buy an apple device and have a decent version of anything you would normally want to do with your computer and apple could guarantee that.
If you look at the games industry where Apple doesnt have any hold, you can see how lacking it is for Mac titles. Developers openly and brazenly dont care about the Mac platform and dont produce for it. That in turn drives every gamer to Windows first. Just imagine that scenario if Apple didnt make these key 1st party products and services? They wouldnt sell anything like the devices they sell.
So yeah, any dominance like iTunes in 2000 is an anomaly (that happened because no other player got their act together and apple had a need for music because it was selling iPods). Generally every product and service Apple has is to protect it's device sales first and foremost. Even as they make loads of money (service division for example), its all in service of selling you thousand dollar phones and Macs. Thats how the business thinks. And its pretty unique to Apple because most companies are split in divisions where each division is very disconnected from each other.