Well you can kind of see the transition away from chariots going on here if you read between the lines a little. First of all, “32 captains” [Dave: Is Steve misreading “32 kings” in 1 Kings 20:1?] may be the equivalent of company commanders; they may even be your “kings” from the earlier question if that term was being used loosely. These guys would be the equivalent of Majors or Colonels in today’s armies. And they’re probably leading foot soldiers armed with spears, leatherized shields and short swords.
And then we have the archers and they have orders to concentrate on the commanders rather than the foot soldiers. So we know archers are a thing. Probably a pretty big thing. They would have fought on foot, behind some chariots, but not being led by ranks of chariots out front like the Egyptians would have done. They’re probably at the rear of the sword/spear men who are doing the heavy lifting.
My read on this passage is that the chariots are assigned to the “captains” and are being used sparingly by those commanders, probably more to direct the troops and keep track of the progress of the battle than to be the blitz force they would have been with the Egyptians. We don’t know the size of the army, do we? But let’s guess it may be 10,000 give or take. 32 chariots would not be a dominant force against a comparable army of the same size. I think they’re there to make it easier for the company commanders to see the fight and to be seen by their troops.
And I’ll just toss this in as a possibility: Is that one reason the Israelites have manhandled the Damascenes? Do they have better chariots? Or better tactics for fighting foot soldiers commanded from chariots? Are those Damascenes not used to fighting without their chariots? Are they not using their chariots effectively? And as for the Israelites, are these guys maybe like the American Revolutionaries of their age; they’re messing up their enemies b/c they fight from behind trees and rocks and don’t fight in ranks like they do in Europe? Dunno. Just a thought.