This is what Spotify used to do (charging $13 instead of the normal $10 to give apple their cut), but they stopped when apple started making apple music available at $10 (since they didn't need to pay their own tax)
You simply can't ignore iOS if you want to have a successful smartphone app business. That fact alone is enough in my opinion to consider Apple a monopoly and to take action to force them to play fair on their own platform.
Abusing market dominance in one sector in order to shut out or outcompete other providers in another sector is the classic justification for antitrust action.
I honestly never really thought about why this is - I simply just hated Audible for it, and thought it was the most annoying part of their app.
However, it's odd - how come the Amazon app is allowed to get away with its own purchasing system?
I believe jordanthoms's explanation is correct.
Deezer music went another route: you can pay for your subscription through an iOS device, but you'll pay a higher price. [0] I'm surprised Apple permit this.
All this strikes me as a clear indication that Apple is asking for too high a cut.
I've never been tempted to use a mobile app to shop on, say, Amazon, but Apple are clearly ok with that experience being far better on Android than on iPhone.
> In my book, the problem is that you are not allowed to provide a link to your payment website inside your app.
Interesting.
The exact words used by the Audible app for iPhone: This app does not support purchasing content. Instead, add to your wishlist.
[0] https://support.deezer.com/hc/en-gb/articles/360000633989