The ideal solution would be Apple fixing that - allowing for a user-defined default player. I'm sad to say it, but if that doesn't become a reality, I may be tempted to switch to Apple's streaming service for that one reason alone.
Apple is intended to be a walled garden rather than a true equal platform for the app devs. As much as I like Apple hardware I hate their mobile OS because of this approach of building special integrations for their built in apps that you can't even remove, while denying other app devs access to the full range of device integration, except if you go through their limited API's.
I would generally agree; for the vast majority of people the "notes" app works just fine, no need to install evernote or simplenote or whatever.
But in this instance, Apple is expecting you to shell out $10/month. I think that likely kills most of the inertia of, "Well, it's on my phone, I don't need another app." I could be wrong, though. Regardless, I'm not cancelling my Spotify subscription anytime soon.
Spotify asks for that too. And unlike Spotify, Apple already has your payment details. You don't even need to enter your password with this thumb thing.
For something like this, yeah, Apple default is probably that strong. Considering that it'll button right into all of their hardware (laptop, iPad, iPhone), I could see it being a fairly significant thing for them. It's one less app to have to use, one less payment interface to deal with, and integrate with whatever music the user already has.
Not to mention that Apple probably has a lot more clout in the bargaining arena with the record labels than Spotify does, and a LOT more cash to throw around.