If instead the DNC ran open primaries in each state with no superdelegates, what would be the point? You might as well just ban parties altogether (for election purposes anyway, caucusing might be a separate thing) and just have regular elections with two rounds. Note that I would prefer this, but I don't think it's what Greenwald is getting at.

Many states require the local parties to pay for their own primaries. Many local parties are bare bones organisations that only ramp up activity every couple of years or so. Voting mechanisms need to be scalable, affordable across a diversity of budgets and technical skill sets. Caucuses, for example, exist because they are dead easy to explain, don't cost any money, and are transparent at least so far as everyone can see who won just by looking around the room.

As far as transparency, that's sort of the main point of the paper: if everyone can themselves check the votes by doing something as simple as looking at something like bc.info, then that imo is a large increase in transparency from the current system which only allows the room-members themselves to verify the results. I agree with you that caucuses in their current form are easy to explain, however I think we can abstract away all the difficult parts and make it a pleasant / easy experience.

I doubt the layperson can understand how that technology works, and that is required for the voting to be democratic: Every voter has to be able to verify that there was no fraud. Not only mathematicians.

There are other countries without electronic voting, but also without the problems of US elections. But since these problems are not seen as bugs, but as features by those in power, I doubt things will change in the future. With or without technology.

This is probably a good point, however this math is at most slightly more unusual than the math behind, e.g. https (which I guess 50 years ago public key cryptography wasn't even invented) and average people are starting to learn to trust that.

And of course, the fact that occasionally some implementations of SSL have been found insecure is in no way an argument to not use it (at least until something more secure is available).