If the customer is using in-App purchases, then Apple does handle the payment, but Spotify actually wanted to bypass the whole in-App purchases problem altogether, so that no additional payment handling cost for Apple would apply, but wasn't allowed to place the link to a registration webpage.
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If I make my purchase inside the app but not pay through my iTunes account, why should apple get a share of the revenue?
You're presenting these as almost rhetorical questions, and on the face of it they make perfect sense, but there is a very real reason why Apple won't let developers bypass the in-app purchase system when users are inside the app - the App Store started with apps that had an upfront price and Apple took a cut, in exchange for running the store (just as every store on the planet does). If they had not made a restriction on using non-Apple payment services in the app, eventually pretty much every app would switch to a model where the app was free in the store, and then you paid the developer inside the app, with all that money going to the developer. And then you end up with a store where every item says "free" on the price tag, and the store owner gets no money for running the store. Such a store does not stay in business very long.
Imagine a brick&mortar store which pays for floor space, heating/AC, lighting, employees, shelves, etc., and has its shelves covered with shiny boxes that have big labels saying, "pay nothing at the register, just take this box home and then send a check to the manufacturer". How would such a store stay in business? They couldn't, it's not sustainable. You can't charge "30% of zero" and make it up on volume.
This is why Apple set the rules that you can't advertise/implement alternate payment methods inside the app. This is also why they didn't make in-app subscriptions substantially cheaper than upfront purchases. Personally, I think 30% of recurring charges is pretty steep - apparently Apple agrees, because they've changed it to 15% after the first year (if they didn't have the "first year" restriction there, lots of developers would say "hey, it's cheaper for us (though a worse experience for our users) if we switch our calculator app to a subscription").
Looking at it as just Spotify, just this once, and without the context/background above, your statements sound reasonable. But now imagine every app takes that approach.
(Also, you seem to have lost the /QUOTE tag (and the brackets around it) between the bit your responding to, and your response - makes it look like the other person wrote it all and you're just reposting - if you edit your post and add the tag, it'd make things clearer.)