Given ancient Assyrian ways of conducting war, you'd have Assyrian kings bragging on their streams about how many skulls they piled up while dabbing on the captured idols of ruined cities to strangely hypnotic hymns to Ashur. Modern norms of war were developed over centuries, and in ancient times restraints were based on material considerations(as someone said earlier) before moral ones. Give the Assyrians nukes, or the Sea peoples AK-47s and they'd do as they did with swords and spears.
Thing is, this creates bad incentives in terms of conflict resolution. If your enemy can expect no mercy, they will show you none. This makes war a lot less "clean" than it otherwise can be. In your scenario, all sides and factions(because it wouldn't just be two factions) would have every incentive to fight to the bitter end, because they could not expect leniency, for them or their family, friends, communities, etc...
There are issues with the Bronze Age & Earlier accounts of battles.
There is a battle in early bronze-age Mesopotamia (the exact one escapes me and I'm too lazy to dig it up) Where both of the kings claimed victory, both claimed to have set the other to flight and butchered tens of thousands of enemy soldiers with minimal loses. The likely loser - the King who put his enemy to flight but was told by his Gods to not go to the enemy city because the land was unclean - continued to rule for several years after, as did his opponent.
I guess what I'm saying is for the bronze age, no evidence of kings collecting skulls for their skull thrones exists, at least at the scale they claim. Battles were likely of much smaller scale than claimed, though no less brutal. Metal was scarce and hard to come by until the late bronze age, and the most common weapon on the battle field would likely have been a war mace.
Which is not the spiked affair we see in europe, but basically a weight (a lump of some sort of slag metal if you were lucky, but possibly just a rock) or even just a straight up club - not the caveman affairs, think like a nightstick or axe handle.
It takes a lot of work and a long time to beat someone to death with a mace, and longer when you'd just got a wood stick.
war ever being 'clean' was a historical anomaly limited in time and scope to feudal europe (and to some extent its colonies) where wars were fought mainly to resolve territorial disputes between noble houses, with the population otherwise completely disinterested and unaffected by its consequences.
apart from that time and place, what people today call 'total war' has been the norm throughout most of the world for pretty much all of history.
It really depends. War in China was all about control of the peasants; over 4000 years it happened, but it was the exception and not the norm. When there was whole-sale slaughter it was usually against a noble family and not their people. We don't know too much about early war in India because reading and writing were hoarded by the priestly class and they didn't carve a lot of stone, but the pre-Aryan civilizations cities do not show signs of violence, just sudden abandonment. In mesoamerica, even the Aztecs preferred to keep tribes under their heel as opposed to outright extermination; somewhat ironically the Inca were more brutal to their enemies, forcing anyone they didn't kill to adopt Inca ways. But this is because the region was resource scarce, as I'll go over down below.
In the middle east, total war was more common because it was war for scarce resources. Life was cheap - even slaves had to prove their worth to avoid the sword. Things were more civilized in Egypt thanks to the Nile delta, but out in the desert, you generally fighting over arable land. If you lost, the good outcome was being taken captive and made a slave by the victors - the bad outcome is being exiled in the desert where if you are lucky lions or wolves get you before thirst really sets in.
So a lot of total war in the middle east was due to straight up ethnic cleansing to expand your people's land, and the defenders having nothing to lose by fighting to the very last.