If Iron is a key factor that turn bronze societies in more ethic ones the change should be observable also from "tribal bronze" to "tribal iron" as is supposed to be between empires, kingdoms and city states transiting the same material revolution.
There can be no perfect match in different conditions. As the most straightforward factor: in order to make it profitable to protect the population, population must produce enough surplus product to make control profitable instead of slaughter. Even the "iron revolution" does not always lead to sufficient profits. For example, if you still have hoe farming on unproductive lands, the result is predictable.
However...
Even more if the iron is truly that significative this "democratic" metal could possibly produce ethic tribal societies even above the level of those of urban bronze societies. These are relevant to demostrate objetive and measurable correlation of "iron=ethics" over the changes between both similar and different kinds and levels of societies.
Actually, where you can trace the written tradition, that's exactly what happened. Moreover, due to the relative scarcity of an already profitable population, the semi-barbarians are at least in one case more humanistic than the Bronze empires. See Zoroastrianism in the ideological plane and Cyrus the Great in the practical.
The changes with the introduction of agriculture or guns could suggest a similar correlation with the introduction of Iron vs the previous Bronze, but it ishould be demonstrated with evidence. So the people suggesting that "Iron reduced the level of violence" should prove it.
These gives even more value to the point to prove this emergence of "ethics from iron" in tribal societies since those also would have to face this supposed necesity to keep the same level of violence... It must be proved, this is how science works.
Uhm… So, on the one hand, we have population growth and direct indications of a change in ethics in historical sources. On the other hand, the statement that ethics has not changed, the change of rhetoric occurred from scratch and at the same time the growth of armies magically did not result in total genocide. Moreover, with an acute desire to cut out the defeated, they were cut out almost to zero in the Bronze Age, and not only on the scale of a separate settlement – see the genetic map of western Europe. The "Bronze Age disaster"
https://en.wikipedia.org/wiki/Late_Bronze_Age_collapse also looked impressive, although military violence is not the only factor there.
In other words, the version of immutable ethics contradicts elementary logic. In science, such hypotheses are naturally not considered as an alternative – otherwise, you can endlessly refute anything.
This is context to suspect something similar but one again appart from help to built an hypothesis, such hypothesis need now to be proved.
It is curious how the mechanism, clearly visible for some weapon revolutions, could not work in the case of iron – despite the fact that for some reason there was no total self-genocide.