It makes voting faster and less expensive (practically free). That means you could have the public voting at arbitrary frequency. You could imagine a system where the public is voting every month, week, or day on what the country should do next.
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.
This is assuming that the system would be inherently trustworthy and trustable with no human oversight. I have a nagging suspicion that over time this system would still settle in a state where we have just as many humans involved in ensuring everything is kosher as we have now, but compounded with a system that is less transparent for someone who is blockchain illiterate.
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.
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.