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- There were other sources of fur on the market. Not a monopoly.
- Not familiar with the New River Company, but color me highly skeptical that this was a genuine market operator with no protections or privileges. If you have a good account of it, I'd be interested to see it. The network effects and high infrastructure costs make utilities especially interesting.
- Standard Oil's market share had begun declining before the Sherman Act passed (https://mises.org/mises-daily/truth-about-robber-barons) and they weren't charging elevated prices anyway. The large market share came from innovation and offering lower prices than others could match. It took a while for competitors to catch up.
- I thought DeBeers did have state-granted monopoly protections. Plus, there are other sources of diamonds, including artificial ones, so the market was pushing towards competition, anyway.
- Not familiar with ASML situation.
So, not even the cherry-picked examples form the pattern you describe. I maintain my "almost always" position. Monopolies are hard to maintain because they create the conditions for their own demise: elevated profits. That is the self-correcting mechanism that you say doesn't exist.
You want unregulated nuclear power plants?
Electricity distribution along with railways and roads and online markets like Ebay are all natural monopolies or duopolies. They tend by their nature to favour the established player/s as the cost of entry is high or intrinsically limited.
The most efficient provision of roads, power distribution and rail lines is via one network within any geography. They do not allow easy entry to new competitors. Established players have an automatic advantage and can and do tend to squeeze out intending competitors due to scales of economy and market dynamics.
Many monopolies have been state-granted, but "almost always" doesn't hold up.
The state is one source of monopoly, not the only one, the market doesn't self-regulate, it concentrates.