> There's an add to home screen button, but it's buried deep in the share sheet and the average user doesn't know about it.

What? It's a single tap to open the share sheet and the button is in the system row "above the fold" (because there aren't even enough items for anything to even be below the fold). If that's "buried deep" I'd shudder to know what you think of uninstalling an application or adding a keyboard.