I would like to elaborate on my point. You don't want the browser to be able to auto-add it to home screen. Imagine if this was possible. Any time there's an ad on a page, that ad would have the ability to add itself, or anything else, to the home screen. Naturally this isn't wanted.
As an example of a good, but unwanted, use. Say I'm reading the Washington Post. Without me knowing, it added itself to the home screen. I may have wanted a WaPo app, but why shouldn't the end user have to click a button (literally, that's it), to add the app. Without this requirement, it could add the app without my authorization, which is certainly not what most users would expect.
Regarding the complexity, can you elaborate on this? It requires less than what a native app requites.
Per it being browser-specific, what else would you like? It inherently has to be done by browser, as they have different requirements.