Ok, I'm going to pick apart your entire post bit by excruciating bit, just like you asked. I will only focus on the sentences that are wrong though.

"There were no taxes and no public services. If anybody wanted anything, they'd have to pay for it explicitly." - Yes, there would be no taxes, that is true. But that doesn't mean there would be no voluntary charities , mutual aid societies/networks, co-op owned businesses, non-profit agencies, etc.

"Ben was as cunning as he was resourceful. One day, he decided he'd leverage his ownership of the river to make a little cash." - Ben doesn't own the river because Ben nor his family built the river. They didn't even build the section of the river their property happens to fall on. Ben owns a logging company. It's possible Ben also owns a forest to cut trees down because his family planted the trees for the sole purpose of cutting them down later. But no, Ben doesn't own a river just because Ben says he owns a river.

"So he built a wall across the river, and put one little gate in the middle. He put up two big signs on either side of the river and said "Because this is my river, anyone who wants to sail a barge from Mises to Friedman will need to pay me a river toll. It's my section of river, and you can't tell me not to build a wall across it and charge tolls."' - Ok, yes. Ben can build a wall and door across a river if he wants to waste his money. Nobody is there to stop Ben from being a moron. Meanwhile, anyone interested in trading between the two towns, will simply go around Ben's dumb wall. Maybe someone will divert the river around the dumb wall and charge less than Ben does. Maybe someone will create a transfer service onshore around Ben's dumb wall for less. Maybe someone will build a road so people don't have to use the river anymore. Maybe the river isn't the only way to transport goods between two cities.

"The bargemen, the farmers of Friedman, and the stonemasons of Mises weren't happy with it, but there wasn't anything they could do about it without resorting to violence (for example, breaking down Ben's wall). They couldn't even apply some kind of self-defense principle, because that section of river belonged to Ben and he could do whatever he wanted with it." - Actually, that section of the river doesn't belong to Ben because Ben didn't build it so yes, Ben is the aggressor in this case if he is restricting people's right to travel freely along a river that Ben doesn't own. Self-defense would actually be justifiable.

"Unfortunately, Ben started a trend. All up and down the river, anybody who owned land on both sides of the river asserted their un-challengeable claims over the river itself, and built their own walls, and charged their own tolls." - No Ben would not start a tend by building a wall across a river, because people who used the river would hate Ben and they would stop buying logs from Ben's logging company. People along the river would not want to jeopardize their own livelihoods in order to build walls. Ben would become an example of how to piss off your neighbors and become an outcast in society. As far as unchallenged claims over the river, again, Ben has no claim over the river, because Ben didn't build the river and neither did his family. No one has a claim of ownership to the natural river.

The rest of your story falls apart there because it would never happen. It then goes into this ridiculous fairy-tale as if nobody in either town could ever possibly find a solution to Ben's wall, or that everyone would just be ok with Ben building that wall in the fist place and simply pay Ben for something they were receiving for free until Ben decided to be a dick, and the even more ridiculous notion that everyone else along the river would be as dumb as Ben and do the same thing he did.