I guess you have never studied physics if you think anarchy is possible. Anarchy doesn't exist in nature.

If you want security then hire private security, or take some kung fu lessons.

You PAY for kung fu lessons, you TAX yourself. But they will come with knives. You buy a knife, they will come with guns. You buy a gun, you TAX yourself. You hire private security, you TAX yourself. Sooner than later private security cartel will put TAXES on you, i.e. higher and higher security bills. Private security cartel doesn't have a NO for the answer in their dictionary.

private companies will compete for your business

Only if there are laws and enforcement to allow competition, i.e. TAXES. Every business tries to monopolize the market.

The world is not black and white, there are millions of colours! Wolves and lions PAY TAXES too. Alpha takes more risks (tax!) defending the pack and hunting, is rewarded with females and is first to eat. Others pay taxes in the form of being next in the order. Tiger is paying taxes, too - if wounded and cannot hunt, he will die; he must be alerted. and take risk himself each time when facing danger. Wolf will get fed by his friends and hunt again, another wolf can spot a bear and warn his cousin.

P.S. Can't wait for ACCS to be fully implemented in bitshares. It seems it is still in the early phases of testing.