I thought the problem was, that their own apps do not have to pay 30%, so they can easily replace any app with their own, if they choose to.
$3 in Apple's bag for no work or effort at all
This is the same sort of rhetoric that calls dropbox a weekend project.
There's credit card costs etc associated with that as well. Doubt it's $3/user per month though and the distribution costs are minimal (only downloads of app updates) compared to the streaming costs (which could be multiple GBs every month).
Spotify: $ to build the app, $ to maintain the music label relationships, $ to manage paying royalties, $ to manage server infra, $ for bandwidth, $ to Apple for the "privilege" of being listed on the App Store and using Apple's payments system (which they have no choice over).
Both companies have the exact same base costs to operate their service. But Apple gets to charge for subscriptions through the app for free, whereas Spotify does not. That's literally the only difference cost-wise, and IMO Spotify is correct to consider that anti-competitive. Whether or not Apple would make more or less money shuttering Apple Music and transferring all their customers to Spotify is completely irrelevant.
And no, I don't consider "creating and maintaining an iOS payments system" to be a part of Apple's costs here. That would exist even if Apple Music did not, and the marginal cost of having Apple Music use that system is virtually nil, certainly not 30% of Spotify's subscription fee.
Some apps pay for that effort with a cut of the app's retail price. Spotify pays for it with the tiny fraction of their users which (a) pay for it at all and (b) pay for it through their iOS device.
No reason to have users pay twice, when they buy their device and when they try to use services on the device they already have.
The cost for the store platform is paid by the developers when they sell the app.
We don't see the internal accounting but it's quite likely they do. Internal revenue distribution is standard practice in almost all enterprises.
This is both true and generally irrelevant for business, except for the particular matter of taxation.