You can recreate almost anything in css/html but you'd have to write a different style for each OS yourself, and it will never match the actual "feel" of the UI. It'll be a little off.

Also, for example Mac OS X has lots of little widgets like the share button.

Maybe someone could make a Bootstrap-like project for these kinds of things?

There's tint2 for doing native apps with JS.

I recently spent an afternoon trying to get a webapp to accept drag and drop emails from outlook. I didn't manage. I am considering making a native app to interact.