IMO it depends on what your running before the anarchy.
If you run a capitalist OS it'd be difficult to maintain lawlessness because of, yes, all that organized crime that comes with it, black markets ect. Those people like rules, rules create markets, markets create boundaries. Just like governments they occupy territory with street soldiers and killers in reserve. Claiming land as their own. Buying land with bodies.
To run an anarchy properly, you need community. Thb you may even need structure at some point, but as long as it remains a decentralized localized collective authority I consider it lawlessness as no one explicitly stated making laws was against the rules of anarchy. Not everyone will choose to abide by these laws and that's why you need community to make these people feel alienated and push them out of the community like a child from a mother's womb. Rejecting those who would be better suited elsewhere. In other communities. Alternatively a loosely affiliated nomadic lifestyle of people roaming, not having any guidelines to follow at all. Free to join as soon as you step away from the clusters of humanity. Until you find you're own little place to carve out that is.
Certainly violence would be a problem, but when is it not?
The point of a strong community would primarily be to retaliate against thieves and strengthen the bonds held by the neighborhood. Effectively enabling the protection (say of women and children) without paying the taxation. Indeed social connection is the a most powerful tool of the people.
Crime would likely be targeted at people who have done something to provoke a grudge if you can wrap your head around that. Generally by the people who cannot be persuaded to live any other way. These people would likely run into trouble more often than others. Putting their lives at risk and potentially causing fatal incidents to occur at a higher rate than say a person raising livestock(doing anything else). Think wild wild west without the need for a sheriff. A self sustaining system of crime and punishment without the need for taxation or military.
No less is desirable. Anarchy is not crime. Anarchy allows crime to work itself out. Which I believe it does. Criminals reproduce with criminals then the criminals keep crime in the family. Then the family has a significantly reduced chance at surviving than a normal family. Seeing as that family has a lot of criminal opponents. People die. Only the strongest remain to profit.
Then only the fittest people, those who refuse to be victimized by the thieves, extortionists, thugs are strong enough to survive the onslaught of fraudsters, scammers with their lively-hoods intact.
Which is where community comes in again. Those willing to work together, like organized criminals, will always get ahead of the rugged individual. Which is why the concept of anarchy as this sort of free for all every man for himself scenario will never work. Because it is already implemented. It's been labeled the free market economy. Fraudsters paradise built of the blood of the innocent. Where cheap drugs and insurance policy reigns over government. The prisons make more money than the artists because of all the return costumers.
The issue is race primarily. You see race interferes with community. Racism causes people to behave strangely and often we have seen nations formed more on genetic (alt. religious) guidelines than physical boundaries. Perceived racial superiority driving one race to ban together to subjugate another. As a unified people or perhaps it just happens by chance, regardless it happens.....a lot. It seems conquering the deep seated race hatred programmed into the administration, prison system and law enforcement agencies is the only viable chance we have at achieving a state of global self perpetuating anarchy.
Anarchy in the modern day. Say in America would be very violent because of the sadism perpetuated by our culture. The hypocrisy and already considerably violent media (socialization) is a bad combo for lawlessness. Oh and then there's all the guns. It would be difficult because our community is shattered and fragmented like our environment. The social atmosphere can be suffocating and it really doesn't inspire what I would call a sense of strong community. Given the loose bonds of trust and overbearing paranoia, yes a lot of people would die if we just up and got rid of all forms of ruling class organization. Eh....
I especially hate it when the police officer tells me I'm driving my car to fast, what does he know?
Yeah fuck that shit.