Full disclosure: I am the technical writer and admin for the @sadkitten down voting bot, so obviously I support down voting / flagging, and here's why.

Down voting is voting, just like up voting. It is an expression of disagreement, contrary to an up vote agreement. But it is not directly a disagreement with the content of a post (though it might indirectly be), it is a disagreement that it should be rewarded. It is primarily an economic value judgement, technically like a public vote on a price. Some other blockchains use betting mechanisms and they are similar, but stake based voting is simpler.

There are three possible states that any post can have in relation to an account. The most common is not voted on at all, for obvious reasons. The other two are having given an up vote or a down vote, which is a vote with positive or negative weight. It is not directly about abuse or content, it is about what should be rewarded. The point is that any and all votes can be cast, and every one is open to everyone.

The Steem blockchain is constantly refilling a pool to rewards which are distributed according the to the system wide free vote. Votes are obviously weighted by stake, instead of the popular democratic model of one person one vote, for technical and political reasons. It basically boils down to that those with the most to gain or lose should have the most say, as their investment is more on the line (skin in the game).

Of course a culture has developed around down votes which see them as abuse flags only. This is I feel to the determent of the larger platform, and it was instigated pretty foolishly by Steemit Inc. as first UI on steemit.com . But it would be in turn foolish of anyone to deny the existence of this cultural view, it informs people's thought and action here. That said it's something I try to bring up and maybe something we can change about the culture if enough people want to.

For the moment down votes flags are used by the majority of people, and especially large stakeholders, to disagree about rewards only in extreme cases. For many this strongly applies to what is trending because of how that makes the platform look to the outside. Jerry's post was one such case, where he had paid to have his very weird post massively rewarded by bid bots, which many whales decided to down vote. As I understand it they didn't think it merited the rewards, and they used their stake to express that disagreement.

In my own work and actions I keep my down voting to the clear abuse categories, at least as I see them. @sadkitten is a bot which down votes the most optimally self voting accounts. These actions are premised on an analysis of the behavior self rewarding which a small community effort is against. My surveys indicate there is widespread support for it, but even still I am personally convinced, though I am always open to discussing it and being persuaded differently.

Down voting is important on a platform which has no official guardians. Introduce guardians, and you centralize the power, which is problematic, arguably more problematic than the distributed stake system we currently have. There have been suggestions of juries and councils before but they would be so difficult to organize and so susceptible to corruption that they are very difficult to imagine working. I have never seen a debate last very long on them. I can dig up some old ones if you are interested.

A last small point, you statement here:

Anarchist derives from the word "anarchy," which is a synonym for "chaos." It's hard to sell people on the idea that chaos is a good thing, so the words FREEDOM & LIBERTY are trotted out to reframe the debate. It's the oldest rhetorical trick in the book, invented by the ancient Athenians.

This is intellectually lazy. You may disagree with anarchism (and I too find it difficult in many ways) but to say the political philosophy of it is akin to chaos is laughable. It is better understood as deeply anti-authoritarian, as anarchism actually means "without rulers". I admire your pragmatic streak (the church of whatever works) but to engage with your opponents you must at least see them for what they are, not some strawman you can easily dismiss.