That's the exact reason they designed it that way.
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.
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.