Addressing the juxtaposition of majoritarianism and horizontalism as natures of democracy, I think they are both accurate and both end up describing what's wrong with democracy as practiced. That is, systems only democratic in their vote-based system of government. Elections feel fair to us in a very simplistic way. There's nothing essentially just about making decisions about how people live by vote other than the one vote per person part of it. If we vote on how you ought to wear your hair, it doesn't change the fact that it's an intrusion (or invasion to use Benjamin Tucker's terminology). In Anarchy, State, and Utopia, Nozick creates an interesting analogy for society with a joint-stock company where we all own a share in one another that forces the reader to face what it means to vote on the decisions that shape someone else's life.
Democracy, when indicating "shared power" exerted directly without State interference, is synonymous with anarchism. When the people are allowed to rule themselves in this way, they learn will learn the value of liberty and the truest form of Self-Government. That's what I see as the true American Dream.
When "democracy" instead is indirect, perhaps in a popularity contest where we determine who wins the right to play the roles of representative and ruler, it's a very poor example of "rule of the people". With voting, we simply play a game every once in a while to choose which kids get to set the rules on the playground and which ones get to enforce those rules. The best part is the lead enforcers pick a very special few kids who get to do to decide what the rules actually mean, and that select few gets to do that for life.
Don't forget, all of these rules were made up by a few guys who took over an interstate trade convention of our initial Confederation. Rather than consensually coordinate trade, which they knew would erode all of their economic privileges, they came back with a proposal to implement a National government over all of the States of that Confederation (co-equal by their language, but with unelected Federal Supremacy in the courts, of course).
But I digress.
As I once semi-plaigerized on the my English teacher's wall (apologies to Alan Moore), "words are the means to meaning." They're the operating system of the internal monologue that makes us human. Those words evolve with us, and through the propaganda of their use, we get to define them and redefine them. I think human history reveals a beautiful story of how we have used language to redefine ourselves.
I think the old Republic died with the Articles. Its spirit lives on, but when we traded the Confederal requisition system for a system of Federal taxation, our States were no longer truly free. Yet, we are still blessed to have the Revolutionary War in our heritage. We rid ourselves of Arbitrary Rule once, and I have faith that we will do it again.
While we must defend ourselves via the ballot, because it does exist, the greatest efforts for freedom will lie in giving ourselves the ability to dissolve the State into the economic organism and the self-assembled social relationships of production. This is impossible as long as the State keeps the economic organism in its control. Its prerogative to define our means of exchange, enforce rights over what is and can be exchanged, give only a privileged few the right to issue that currency, and then tax us in that means for the right to produce has us hopelessly ensnared beyond the wildest dreams of the men who once rebelled against Ole George.
I'm inclined to agree with the idea of Exodus. I don't think the State will lose a direct fight. It was created to be the most efficient fighting force. The British Empire lost America because it wasn't worth enforcing their formerly assumed rights, and they couldn't eradicate a guerilla population effectively.
I think that is what the path to anarchy will look like. More and more people will choose to give to Caesar what is truly Caesar's - nothing. If Caesar protests, he will find himself with nothing at his disposal but his complete personal freedom.