Bronze was expensive. Only an aristocratic warrior caste would have bronze swords and armor.
Carbon steel would have made weapons cheap enough to make, that a whole tribe could be armed. They could thus outnumber the Egyptian warriors. That could also explain the drawings of families: the whole tribe would have been in migration. The technological breakthrough of iron would mean that they could overrun older societies.
IIRC, the Hittites perfected carbon steel for swordmaking & the Egyptians knew their copper swords were no match.
I don’t know about bronze being expensive. If anything, iron and steel are more labor-intensive and technologically difficult to manufacture, so I’d say they were technically more expensive.
I *do* know, however, that once forged, steel can destroy bronze implements and stay unscathed. In other words, it’s much harder and stronger, and thereby gives anyone armed with steel weapons a very substantial advantage.
An army with steel weapons against a bronze-armed foe would be practically like bronze-wielders fighting unarmed men.
I did a little research, and it turns out you, elcid1970, and I are at least partially all correct.
Here’s a high-school level lesson on the subject:
http://study.com/academy/lesson/iron-vs-bronze-history-of-metallurgy.html
It turns out that tin was relatively rare. When a lot of trade routes were eliminated (for whatever reasons), tin couldn’t be obtained easily, so metalworkers looked around for substitutes. The Iron Age was born from their efforts.
Iron ore was plentiful, but hard to smelt and process. Nevertheless, human ingenuity prevailed and steel weapons (along with other handy implements) were invented and turned out to be even stronger and better than their bronze counterparts.