There's always more to say, but u/Brigantus (now a deleted account) contributed answers to this thread, and this one, to answer exactly this question. The important things I think to add are that Brigantus put too much evidence on their origins as Prehistoric classifications and the Classical inspiration for these classes. First, they are obviously not purely prehistoric. Historians continue to use them to describe well documented periods of history, particularly in Greece, Egypt, and the Near East regarding the transition from largely bronze tools to largely iron. That conveniently coincides with the social turmoil from c. 1250-1050 BCE, which probably encourages using the Bronze/Iron divide to appear to stark in that region.

Secondly, this system of [pre]historic classification takes clear inspiration from the Ancient Greek author Hesiod, who described the history of mankind up to that point as a mythical Golden Age, a mythical Silver Age, a Bronze Age (which roughly corresponded to our own idea of the Greek Bronze Age), the Age of Heroes (a mythologized version of the Greek Dark Age and the setting of most myths of heroes like the Trojan War), and the present (for Hesiod) Iron Age. It was a convenient framework to inspire modern scholars.