Of course webpages would still be around and needed, and desired for more basic content, but by the time you want to offer something as complex or regularly used as Facebook or Twitter or Reddit or Soundcloud and so on, it'd be better as a native app, as the current native clients for each of those websites already prove.

I mean the UI is undeniably smoother, and they can seamlessly hook into the OS notifications systems and better multitasking (for example I see separate entries for each native app in the OS's task switcher, but have to go through the extra step of switching into a browser then its tabs for webapps) and energy saving and everything else.