Apple is actively refusing to implement the standard for installable webapps (PWA). So, Apple is intentionally crippling a feature on the grounds of privacy with no possible remedy.
This decision comes from an actor that is protecting their business interests. It might have some positive side-effect for some users, and of course Apple will spin it that way. But in the end Apple is very agressively hampering the web's progress to get their sweet 30% cut.
Note that Apple does support PWA to some degree. My understanding is that they don't support onbeforeinstallprompt, which means you can't create an ergonomic, in-browser installation flow. You have to manually go in the browser menu to find an "Add to Homescreen" button, or something along those lines.
Installation of web app performed by bookmarking it or by pinning it to home screen. That's performed by explicit user decision and must be honored by browser if it wants to make a distinction between random website and useful website.
Not sure about pinning, but bookmarking should not grant any extra rights. Even the useful websites should not be able to track me forever.
Look, we already have lots of website prompts, like camera and location. The best thing, privacy-wise, would be an explicit prompt: "this website wants to store information, possibly including tracking identifiers, forever. Allow?"
If browsers asked approval before using localstorage, we wouldn’t have this decision.