Yes. For several reasons: The most important of which is, that we are not always online. Be it because we simply choose not to be, because we want our goddamn peace for once, or that we're actually in a place or situation with no internet connection. Sure, some webapps work offline as well, but it won't be the majority, exactly because an always-online state is assumed.

And even though performance is usually not an issue, battery life is. And most browsers introduce more levels of abstraction than are necessary for the application at hand.