I agree that the example website is light and it wont take very long (not double the time) to make it scale. For the bigger sites with much content especcially built several years ago it might be a challenge to build a nice readable RWD.
Myself I often read on mobile and I appreciate when the site displays well. As a designer I almost always implement a responsive grid. For an app that is targeting mobile users I would not rely on resposive web but build a native app of cause. I do believe that users deserve a great experience on mobile and tablet devices.