A good idea, but not so easy to achieve. Currently I’m working on hiding certain blocks when the screen size changes using css. Its certainly the easiest way to do it. But not so easy to make it configurable.
In some cases the blocks will also need to be redesigned to allow for less information to be displayed on small screens.
I think if you look at each block in turn it is easy to see which ones simply don’t work well on small screens.
I would expect many sites would not go to the trouble of deciding for every block if it should display on small screens or not.