Faced with the alternative of 133 pages, I opted for the video after all! It was quite fascinating and gave me a much better glimpse into how anarchists think it might be a better system, thank you. I was especially intrigued by the idea of, in effect, doing price discovery on my legal values: "I am firmly opposed to all torture, but I guess I could go with the Rights Enforcement Agency (REA) that tends to contract with arbitration courts that allow torture to death, if it saves me $7,566 a year ... but not if it saved me only $7,528!"

I still have major hesitations, though perhaps those too have answers. I'll sketch them here in order from least to most worrisome. Maybe I'll try to make a separate post on them.

1. The practical burden of all this research into the various "laws" available: IIUC, I have to know all the many competing REAs, their favored Arbitrators with each of the other REAs, how each of those Arbitrators tend to settle, and who all the other people I might interact with contract with. (I can smoke tobacco around this friend because their REA did not negotiate against second-hand smoke, but not around this friend and this friend ...) Especially when it's not at all clear that the information I'm getting is any good. Back when I was a libertarian I tried to imagine private alternatives to the FDA, and it ended up so convoluted I had to think in the end it was something of a natural monopoly. It may sound whiny but I'm really not sure it's workable. I'd have to hire some firm to decide what firms to hire, and find a way to figure out whether that firm is actually acting in my interest ...
2. Letting laws be determined by market forces basically means the rich get to set the laws; if I am rich enough to contract only with REAs that will ruthlessly pursue the interests of their very rich clientele (to violence when necessary, even assuming violence is "more expensive"), then I can have my way and get richer; if I am too poor to afford an REA who really can defend my interests then of course I'm just going to get poorer (if I'm lucky). Perhaps many libertarian/anarchists types think this is justice - that rich should make right - but I think it's far from the case.
3. "Rich makes right" still sounds a tiny bit better than "might makes right", even to me, but I still don't see why it wouldn't devolve into might makes right again. We are supposing there are powerful agencies out there to protect interests. Why would they be happy with salaries from the very rich who do not already have their own armies? Why wouldn't they simply take from the otherwise defenseless rich? Because violence is "expensive"? How expensive is it to take from someone defenseless? Would that REA be shunned by others? Sure, but if they're powerful enough, it doesn't matter, and if they're not powerful enough, then the same problem repeats with that more powerful REA - why doesn't it just take what it wants? We need to band our non-looting REAs together into one, to protect group interests? That sounds familiar.

Anyway I have more to think about, thank you. Though I still think anarchism would be even worse than the imperfect system we have now, I have a better idea of why some think otherwise.