If the state were to suddenly disappear, yes, I'd agree with you. Humans have existed for hundreds of thousands of years, most of that without a state, and with many groups living in what were likely arguably something like anarcho-communist societies (check out The Dawn Of Everything from David Graeber). Warlords are a symptom of a power vacuum.

what you are describing is the tyranny of structurelessness

and you are correct. structure is impossible to escape. but general hierarchy is not. I'm defining that as a structure in which one party has general powers to control another party, like police.

the opposite would be specific hierarchy - a structure in which a party has power over other parties only in prescribed circumstances, like a bouncer deciding when a person must leave a bar. within the structure of our society, that bouncer can't leave the bar and start forcing people into or out of other locations. a cop more or less can do that.

therefore, it's not a given that a "nonhierarchical" society is one of implicit structure. the most successful "nonhierarchical" society would be explicitly structured and would have robust checks and balances through specific hierarchies.

for example, a subject matter expert should probably have preferential influence on decisions within their subject over non-experts. certain amounts of violence may always be necessary, so perhaps certain resources need guards. those guards would not be deciding policy, but they would be administering a pre-designed system of resource access, with the power to enforce that system if someone is trying to hoard that resource. (I'm not certain force will always be necessary, but it's perfectly believable.)

the best structures would discourage power accumulation with distributed responsibilities and self-improving systems ("laws" that prescribe their own revisions, theoretically with certain provisions that prevent regression toward allowing power accumulating behavior). these structures are not impossible, they're just difficult to design and they are typically hated by power-seeking parties.