Chariots go back to the Bronze Age. To extend your analogy, charioteers were the fighter pilots of their era - a loss of even one was a blow militarily and financially.
There was a whole logistics train of chariot craftsmen, etc. to maintain them, and charioteers took decades of training to master fighting from them.
The advantage of the chariot was that they travelled twice as fast as the average soldier, but if your soldiers could run fast while fighting, that advantage disappeared.
(There's speculation the Seas People, who were involved in sacking all of the major cities of the time, could run.)
A century before the "Catastrophe" of ~1190 BCE, when all the cities of the Mediterranean were sacked, northern Italy began exporting iron swords. Around that time, also, tactics were worked out using a small javelin unskilled soldiers could each carry a bunch of.
The city would have a standing army of 1-2000 charioteers, whose speed gave them a big advantage on infantry. But 10,000 infantry armed with iron swords, and with javelins to take out the horses, could easily overwhelm them once they were on foot.
It is not hard to imagine a band of adventurers recruiting from oppressed people surrounding each city by promising spoils, sacking it, and moving on to the next.
The "Sea Peoples" is largely a modern invention. The only contemporary mention was the Egyptian account. An invading force arriving by sea didn't really tell you much about their regular culture.
Egypt could field a lot more troops than any of the city-states that were sacked, so survived to write about the experience.
There was a whole logistics train of chariot craftsmen, etc. to maintain them, and charioteers took decades of training to master fighting from them.
The advantage of the chariot was that they travelled twice as fast as the average soldier, but if your soldiers could run fast while fighting, that advantage disappeared.
(There's speculation the Seas People, who were involved in sacking all of the major cities of the time, could run.)