Yes, you technically have other music players, but they're not as integrated into the OS as Apple Music is. We picked Apple Music for this reason, even though it's a rather bad UI.

Same with Maps. Not that I want to give Google more of my location data but others that want to use Google Maps as their default maps app, can't right now without all kinds of third party hacks.

So yes, the competition does exist, but due to deliberate actions BY APPLE to stifle their APIs to keep them heavily restricted, these apps really aren't first class citizens on the OS.

I largely favor Apple's approach of minimizing data sharing, but their apps are often inferior to the third party alternatives. They should use their app store stick to instead have a MFi-like certification program for data. If you want to be a first-party app for Maps, Mail, locations, etc, you have to demonstrate that you won't abuse that data, and have the right infrastructure to protect it.

Update: Look at web browsing. All those browsers use WKWebKit, so they're all actually just Safari. And Apple's fine with telling the public that they have choice here. That's just blatantly false, and I don't see how their legal team allowed them to make such a statement.