Because pure iron, with no carbonization, is useless as a material for tools or weapons.
Carbonization was invented/discovered after the Bronze Age collapse, slowly over hundreds of years, exactly because they didn’t have access to bronze anymore.
Are you suggesting that you disagree with the author's thesis and that iron wasn't a contributing factor or the major one?
Despite being "useless", almost all early iron age weapons were iron, not steel nor bronze. They generally knew about steel, but could not control the carbonization well enough to outfit the whole army with it. Steel did not become widespread until the Roman era.