Even then, there's a lot of feature you end up missing out on. Even just basic navigation has to be done via the browser's default navigation options. Even simple things like long-pressing something on the page will typically only give you access to your browser's long-press menu (though that's not always the case, in my experience very few web apps handle this effectively).

Personally, I prefer the experience of a native app. But I get why it's not appealing to all people.