This narrative fits with the argument that I've seen that States were more appealing to the elite in non-state societies than to the average barbarian as non-state peoples were more free and healthier.
But is that really the case in every known example?
At the risk of seeming flippant, what is the definition of "state" that you're using here? The question is not trivial. In the first place, what Modern historians and Ancient historians call a "state" is very different, and even without worrying about the way the nation-state has permanently altered the way we think about such things it's come to my attention fairly recently that even late antique historians and medeivalists think of the state differently than ancient historians or students of the early modern period. In the second, the logic seems circular. From what you're saying you seem to be thinking of the state as a socio-political entity with a set legal, or constitutional maybe, framework established fornally, rather than by tradition. By definition such a formal establishment would occur through an individual or group of individuals, since we would have to discount most other forms of gradual development as being essentially traditional. So then the reasoning would be circular: states are defined by this sort of formal establishment, ergo this formal establishment appears in all states.
In addition to that it's worth pointing out that many of these supposed lawgivers are legendary or semi-legendary. Even in cases like Cyrus or Solon that are certainly historical there's usually little reason to take the later mythologized version as indicative of anything. These are semi-legendary figures and the sage lawgiver is a literary figure, not a historical one. Nor does it seem to me particularly persuasive to define the state by the arrival of some lawgiver, which as I've already said is circular. Solon, for example, established a new system of laws for the Athenians. But they already had laws and a social structure underpinning them. And even before that they had traditions and structures, on which their later laws were based--the organization of citizens into tribes and so forth did not just pop out of nothing. So where does the line between traditional,social structures and "the state" get drawn? There's not much in the way of recognizable constitutional theory here, the beginnings of that are usually said to come from Plato and Aristotle
There's a lot more that could be said here, and it's likely outside the realm of any single historical specialist, but I don't think the question really makes sense as stated