For such pure democracy to be useful and desirable, the units of governance should be reverted to city-states, in which the citizens share common traditions and common problems. The European national state, or the US and alike are just too big for this. I live in a national state, and even after ethnical cleansing about the beginnings of 20th century, and years of fascism and social engineering, the state is too big to be able to peacefully agree on sth. in a way that nobody will feel out.
Now, I'm in favour of city-states, but I do know that it's only a daydream.
Postscript: I think that the US is sort of like the continuation of the Empire. D.C. is the new Rome. And it is indeed sort of a Senatus populusque americanus, in that people rule the state. But as Aulus Gellius says, here, people means patricians.