If you think the bulk of users even know what "share icon" is you're kidding yourself. If you think they find that modal window intuitive you're kidding yourself. Even then, you're sharing... to the home screen? "Share to the Home Screen" is not the way anyone thinks about installing an app. The whole concept is a mess.
So you’re saying that you’d like to send web notifications to users who aren’t “technical enough” to add a website to their home screen? Surely then they are also not technical enough to unsubscribe from these spammy popups. I am glad that Apple protects my mom from this nightmare.
That's what I'm saying about device variation: that downward pointing arrow would be incorrect on an iPad because the share button is in the top right. Exactly how far from the right depends on OS version, whether the screen is portrait or landscape, whether you have a larger text size enabled in accessibility settings...
And _all_ of this is ignoring the fact that Android also exists. Half the point of using the web is to be able to do stuff cross platform, once you start sniffing user agents and screen dimensions you're creating something doomed to fail in the long term.