It seems like you also need to re-evaluate against pretty much suicide infantry.
You have to account for the possibility that for your enemy losing a couple of regiments for a town of 10,000 is acceptable losses.
And of course it wouldn't work if the commanders didn't have informal authority to put their soldiers into pits or summarily execute them - also well documented.
The Aztecs and other ancient people like the Vikings didn't make excuses, they made war for it's own sake to please the entities they were worshipping with the blood of men.