You ask what problem would be solved, and then give an instance that I think it would be least effective for. Well here are a list of problems that I think this would be good for.
Now one point I should make. I structured the proposal explicitly with the idea that the vast majority of your votes remain anonymous, and of the fraction that do not remain anonymous, you get considerable choice. I think that the privacy issues are preserved. What has changed is that there is some accountability for the "faceless hordes". Is that worth potential for conflict that comes with accountability? I think so, but then again I was on the wrong side of the current system right at the start, and in every case where it has been argued, I have been on the side of making things more accountable...