You aren’t the only party in the transaction. There’s also the entity providing the application in the first place. Don’t use loaded phrases like “none of their business” which make the privacy wonks start salivating when that’s is not what this is about.
The point is that if I'm buying an app from, say, some Facebook store to install on my iPhone, Apple is not involved in this transaction, so they shouldn't get a cut.
Sure. And you'd think that is built in when an IOS dev pays their $100/year licensing fee.
If not, I wouldn't be opposed to the paying to review apps outside of the App Store (where their 30% cut assumedly takes into account for App store apps), as long as the review is purely for security and not to comply with App Store rules (since I am not hosting it on the app store). But charging everytime someone download a semi-popular app, or worse, updates that app (since the install fee is per year) starts to go beyond "what value am I bringing to this feature?"