>People think that without government, the world would be in complete anarchy, when the only examples we have close to that show the opposite
A) The old west DID have a government. The US government wasn't exactly helpless out there.
B) If you want an example of an area without a government, the best example is Mogadishu between 1991-2006.
Towards the end of anarchy they had reliable and dirt cheap cell phone coverage, internet access and imported goods were often very cheap (no import taxes) and they had multiple, cheap competing airlines.
The roads were terrible though and you would often be charged for using them (between $3 and $300 depending upon your cargo). According to the BBC there were 7 checkpoints in the 50k stretch between the airport and the city.
Dire poverty and unemployment was the norm and the need for security dominated most people's lives. They largely relied upon remittances to survive.
While there was no national government with a monopoly on violence Somalis reverted to clan based quasi-legal structures to mediate disputes, which was ineffective at mediating disputes across clan boundaries.
The society demonstrated that anarcho-capitalism (or the closest viable approximation) wasn't entirely dysfunctional but it was clearly pretty awful. Life is much better there now. The roads are higher quality and don't have checkpoints any more. The need for security doesn't dominate people's lives. The economy is growing again.