>>58484
Nobody can know how they will function. We can only offer conjecture based on economic and historical insight. I think the private development of rails may shed some insight into hypothetical AnCap infrastructure development, but the actual process would be shaped dramatically by so many things, including whether old cities were being updated or entirely new ones were being constructed, where it was happening, the dominant industries of such a region, the circumstances of the privatization process, and so on.
>>58485
Some of them were. Other lines were constructed privately, and they performed very well. The attempts to regulate the rail industry didn't take at first, either. I'm trying to remember which of the books in my collection goes into the history of this, but basically there were successful private rail companies in services alongside the state boondoggles.
>>58495
I would point out that your objection seems to suggest that transportation infrastructure has to closely resemble what exists today. Modern road networks are thoroughly influenced by state meddling. It seems possible that the majority of logistical needs could be met in some regions through rail transport. Such cities would naturally look very different, but suggesting that trains couldn't fill a comparable niche to automobiles suggests a lack of imagination. That said; I don't think the 1800s-1900s rail networks are likely to fit the bill for such a hypothetical situation.