How do you explain this theory that they care about the store and don't care about web apps, if web apps allow both developers and users to skip the store?
They care about the store primarily for some other other reason, and the fee is just incidental they don't care about? I say, "Unlikely".
If that was the case, then why did they ever create the store in the first place? They started out with no public store and all installed apps were fully internally owned and controlled. If they only cared about that, they already had that before creating the store. If they only created the public store to allow a wider range of other apps to exist for the users, many years of prior examples of external apps that a device/os vendor could support without caring about controlling or extracting a fee from existed already from PalmOS and WinCE etc. They didn't need any store, or they could have allowed a 3rd party to operate a curated convenient store, or they could have just maintained a directory that had listings that pointed to all the random apps on their own websites etc and the end user experience could be exactly as smooth as today. The os and the app package format could provide all the same user protections and procedural consistency.
No, they only care about the app store for 2 main reasons:
1 - Because other platforms were already more useful to users like Palm which already had thousands of unpredicable random special purpose apps for many years, and so they were simply required to provide some sort of equivalent facility whether they wanted to or not.
2 - To extract a fee from all of that activity.
Once web apps allow both developers and users to skip the store... then what? Apple still doesn't care? No way. Come on.