The single click Home Screen is definitely a platform limitation and not a technology limitation.
There are dozens if not hundreds of Real world examples where companies moves to Web Based technology ( example Ikea ) and move back to Native App simply because the experience, and user retention rate is far higher in Apps. React Native is bridging the gap but many would argue that is Native as well, not Web.
I am not in support of everything App Store. I think there needs to be a balance of things. I think there needs to be an option for user to install ( or sideload, which is a word I hate ). What we dont have an answer is how should Apple monetise what ever they think is needed for their R&D cost that is also acceptable to user and developer.
[1] https://www.destroyallsoftware.com/talks/the-birth-and-death...
Icons are an artificial limitation. Ditto for the app store (access and distribution via web are much easier than an app store, and curation could fulfill the trust aspect).
Technology-wise, there's no technical limitation preventing a web app from sending instant messages. We are, however, hampered by the adoption of browser support for things like cameras, gamepads, etc, but even there, much of that is policy, and not due to how long it takes to integrate with browsers.
Games/performance are the one thing that's true here, though it's possible WASM will upend that, too.
The app stores taking sizable cuts of the profits provide a strong incentive to prioritize apps over web, and drag their heels on supporting web apps.