So what problem does it solve? What does the blockchain accomplish that a paper ballot does not? And what are the costs in terms of user interface and voter education, relative to paper?
I'm not saying this would be good necessarily, only that such a technology would enable fast, frequent, continuous control distributed across the population. Such a country would be very different from anything that exists today.
Assuming that voting would become effectively free, the second point does sound quite intriguing. It's the sort of direct democracy that is practiced by some countries (e.g. Switzerland). It does require a certain level of voter education though - so people look at the longer term. Otherwise you'll never push through an initiative that raises taxes for example.