That is why the disappearance of bronze should not mark the end of the age. Rather the appearance of a new metal (iron) or rather the ability to obtain it in quantity and the ability to smelt ore into ingots and work iron ingots into tools, should mark the start of the new age.
No, that’s why the use of the terms Bronze Age and Iron Age should be tipped onto the refuse pile.
Iron implements, components, tools, and weapons have been showing up in very old contexts since the beginning of archaeology. Iron was used alongside bronze, but processing iron from ore was done by various means discovered independently by different cultures. Meteoritic iron (which is generally nearly pure iron) probably accounts for most or all the seemingly anachronistic finds.
Bronze continued in use from the so-called Bronze Age (which includes the Mycenaean era, when armor is described as being made out of bone, leather, and other materials) right up to the present day, essentially without a break.