My criticisms of the ancap system:
1-Nothing will prevent monopolies and companies would quickly become feudal states.
2-There would be no institutions such as basic sanitation.
3-The poor, especially beggars, would not have access to health, public safety, education, firefighters, etc. (or they would become extremely indebted).
4-Everything would become more expensive, companies would charge more for basic services, health, safety, firefighters, education, every street with a different owner would have a toll, etc., because companies will always aim for the maximum profit possible following something similar to Laffer's law.
5-The system of laws only works in a territory controlled by a "coercive force".
6-Labor laws would end and nothing would prevent slavery.
7-The principle of non-aggression defended by Daniel Fraga is completely utopian and would never work in real life, it is as fantastical as communism. 8-Ancaps argue that everything that comes from the market is good and that companies that sell bad products will naturally be replaced, but this is a naive and fallacious way of thinking. In today's world, we see several companies that sell products that are made to fail and continue to operate and have influence in the market (research planned obsolescence). Furthermore, without government intervention, large corporations would be able to dominate coercive power and would soon be able to exterminate the competition by force or with sabotage tactics, media manipulation, etc., in addition to being able to use cartel tactics freely.
9-The justice system would become completely bogus, all "justice/law firms" would have owners and soon these would become untouchable by the law.
10-People may even be able to move to more favorable regions, but this process will always be costly and many people will not have the chance to move. 11-The system as a whole would scrap human and labor rights, only to favor the richest people and would certainly quickly collapse with popular uprisings, returning to classical States.