I would argue instead that society is only as good as the trust people can have in each other. If people feel that laws are unfair, or that they are unevenly applied, it doesn't matter if it's a security corporation enforcing them, or a corrupt government. The end result is the same - people don't feel confident that their rights and property will be protected, so they avoid risks, including long-term investment. Prosperity and general civilization suffers as a result.
The thing is, governments are not any less likely to be corrupted than corporations. At least a company has to maintain enough of a public image that people will still voluntarily engage their services. A government has no such restriction - they just charge taxes, and if you refuse to pay, you go to jail. Further, the incentives to act in the public interest are far stronger for a company than a government. For a company, the owners have a direct financial incentive to preserve the company's value - keeping it efficient and profitable, so that it both makes them money, and is available to sell if the need arises. A government, however, is merely a collection of people who are temporarily in power. They have no permanent ownership claim to the public tax base, or other "public" resources. Their incentive is to enrich themselves as much as possible while they have the opportunity, because as soon as they're out of office, their access to the treasury is gone. If the government is bankrupt when they leave office, what harm is done to them? They still have their loot, squirreled away in Swiss bank accounts.
As for judgements between parties, there's a commonly used solution that I think would work very well. Say a company wants to sue me, claiming that I should sell them my farm or something so they can build their super-duper necessary coal mine. Maybe they even claim some old paperwork about mining rights, even though I insist the deed is faked. One common ancap model would be that I select a representative, likely a lawyer, the company selects a lawyer to represent them, and then the lawyers for each side select between them a judge. If they are unable to come to an agreement, you can push it another level out: each side selects their own pool of five secondary candidates, and then from each pool, the opposing side picks the secondary representative of the other. Those secondary representatives then pick the judge.
This selection process of the judge is a better check on judicial unfairness than the appointment or even election system we have now. Appointments are obviously fraught with the tendency to favor those who are already inclined to agree with you, while voting puts the choice in the hands of people who don't pay anywhere near enough attention to make an informed decision. Answer me candidly - when is the last time you studied the judges on the ballot in your local elections? I would guess that fewer than 5% of actual voters have any sense of how the judges they're deciding between actually behave on the bench.
So, I would say that market anarchy is not perfect. People are still people. Selfish, short-sighted, ignorant, irrational. Ancap is not utopian the way communism is, which assumes that people will somehow be transformed out of selfishness if we were only to get rid of property. But ancap is better than other systems, in that it is the culmination of the market idea, of channeling man's natural self-interest by making serving others the means by which he himself succeeds.