Anarchy is "a political theory holding all forms of governmental authority to be unnecessary and undesirable and advocating a society based on voluntary cooperation and free association of individuals and groups." (From Merriam-Webster, via Wikiquote.)A group of persons consists of a voluntary association as long as each member of the group is free to leave the group. The fact that leaving the group might result in a hardship for the leaver (e.g., relocation to an area with less fertile ground) does not negate the group's voluntary character. Those who choose to stay do so because membership in the group best serves their interests. Acceptance of annoyances (e.g., noisy neighbors) in return for benefits (e.g., division of labor) is simply an inescapable fact of life.
. . . The word "anarchy," as anarchists use it, does not imply chaos or anomie, but rather a harmonious rulerless society. However, ideas about how an anarchist society might work vary considerably, especially with respect to economics. Also, there is disagreement about how a free society might be brought about. (From a Wikipedia article about "Anarchism.")
The state is "the group of people comprising the government. . . ." (From TheFreeDictionary)
Politics is the process by which decisions are made within groups. Although the term is generally applied to behavior within governments, politics is also observed in all human group interactions, including corporate, academic, and religious institutions. (From the Wikipedia article on "Politics.")
A group of persons may be said to live in anarchy only if all of the rules that affect everyone in the group (e.g., where to live, how best to defend the group against predators) are made by unanimous, informed consent, which might be tacit. It follows, then, that a group might -- by unanimous, informed consent -- give a subset of its members the authority to make such decisions. The group's members might delegate such authority, willingly and unanimously, because each member believes it to be in his or her best interest to do so. (The reasons for that belief might vary, but they probably would include the notion of comparative advantage; that is, those who are not in the governing subset would have time to pursue those activities at which they are most productive.) With a governing subset -- or government -- the group would no longer live in anarchy, even if the group remains harmonious and membership in it remains voluntary.
The government becomes illegitimate only when it exceeds its grant of authority and resists efforts to curb those excesses or to redefine the grant of authority. The passage of time, during which there are changes in the group's membership, does not deligitimate the government as long as the group's new members voluntarily assent to governance. Voluntary assent, as discussed above, may consist simply in choosing to remain a member of the group.
Now, ask yourself how likely it is that a group larger than, say, a nuclear family or a band of hunter-gatherers might choose to go without a government. Self-interest dictates that even relatively small groups will choose -- for reasons of economy, if nothing else -- to place certain decisions in the hands of a government.
All talk of anarchy as a viable option to limited government is nothing more than talk. Empy talk, at that.