Artillery did shape warfare for a while in Europe in 19th century. Cavalry attacks were used to force opposing infantry into defensive squares and then these high concentrations of troops could be pounded by artillery. Of course, Wellington was able to somewhat overcome this problem by using the reverse slopes of hills at Waterloo (protecting his men from any follow-up artillery fire).
Having never read the book, I'm not sure to what extent the author means by 'primitive' but if we say that Rome was primitive then his argument does not hold because the cohorts of a legion operated in tight formations and therefore would be vulnerable to bombardment, whereas, something like the Golden Horde would fare much better because it was primarily a cavalry-based army with great mobility.
I'll use his own words to define what he means by primitive:
"The term
primitive, when used in its usual sense on anthropology, merely refers to a technological condition - that of using preindustrial or preliterate tecnology. In social terms, primitive refers to societies that are not urban or literate"
So both Rome and the Golden Horde were not primitive by this definition. Keeley is a professor of Anthropology and his thesis is, as the title suggests, to explore the idea that perhaps war was common pre-civilisation i.e. before Sumer, Ancient Egypt and the other river civilisations, where really all human societies could be classified as primitive.
As for your Roman example, I have no doubt that, on occasion, artillery was used in ancient warfare in field battles, but generally, as Keeley himself points out, artillery was by far most effective against fortifications and I'd expect that's where it was mostly used. It was expensive, heavy and therefore generally immobile - you'd bring it to siege not fight pitched battles in rough terrain.
As technology moved to cannon and developed, this position changed and it became worthwhile for a field army to have artillery (at first for shock and awe, rather than any decisive use on the battlefield - again they were far more effective at knocking down castles and walls). But that changed in the 17th and 18th century - look at the Swedish innovation of small horse drawn gun batteries that could be effectively moved quickly to take advantage of battlefied situations) However again as the battlefields expanded and gunners lost sight of their actual targets, in the 20th century, the accuracy of artillery plummeted.
I get what you've presented and don't disagree with the premise presented (using Indigenous Americans as the example). That said, considering Verdun's rolling barrages during advances against static/grouped forces, it might be a bit more that 'lack of artillery in volume' was more an issue when dealing with dispersed groups... though, the tactics change. To make the point using longbows and arching shots... if you choose the location wisely drawing the enemy into a narrow pass/area as they attack concentrating your fire, or have your archers advance with you providing a rolling wall allowing your troops to get closer, then you have an advantage. Naturally, both cases demand a significant volume of fire.
It can also be used to deny the enemy access to a particular area. Sea lane fortresses are obvious, what isn't, again using archers, might be ensuring that no one can pass through X area, so they take Y route where you want them (much the way Mustard Gas (liquid) was used in WWI, mines since). In all cases again, however, it requires a change in tactics and a volume of fire which also must be sustainable.
K2
The point about Verdun that I omitted was that this was the 'greatest artillery battle' ever (I paraphrase, but I think it's true.) Keeley states that 200 rounds of artillery ammunition were fired for
every casualty in that battle - I assume combining both sides
. Other sources for the battle of the Somme have higher figures of 250 rounds of British artillery ammunition for every German casualty.
Remember these artillery barrages are against large numbers of static forces. i.e. the ideal target. Yes they are in fortifications - but then, well, you would be, right, if you were ordered to confront the enemy and not to give up territory and faced such technology? So the point he is making is that in the face of a mobile, dispersed enemy who doesn't care about 'holding land', artillery is pretty much useless. Yes you could theoretically build up sufficient artillery forces to pound a tribe that is facing up to you, but you'd need
a lot - remember, at their pinnicle of use in Verdun, even taking into account fortifications, they just weren't that accurate at all - so by the time you build up enough, the enemy could easily move away, thus making such weapons highly ineffectual. Today with drones, guided missiles, ground attack aircraft and as Keeley puts it 'electronically-assisted artillery' etc. this accuracy issue has subsided somewhat.
As for the examples you bring up, they are tactics. Primitive warfare very probably used bottlenecks and other such tactics when the situation allowed them. I disagree with the 'rolling barrage' of arrows, however. This seems to be an extrapolation of a modern technique, but doesn't make sense in the primitive world. One has to assume that both sides had archers and other types of missile weapons. So advancing your own missle troops into the enemies zone of fire, effectively giving the enemy a load of free shots at you would be highly risky...
...Because, before you point out things like armour, Keeley is talking about primitive warfare and there are significant differences - essentially there was no armour. Quilted cotton armour was effective at stopping an atlatl as the Conquistidors found out and against an individual arrow, a variety of materials could easily stop it penetrating and make it merely bounce off if you had metal armour, given that arrows are quite light - especially at a distance. (Of course then that's why you wanted to fight huge numbers of arrows into a concentrated space, a la English Longbowmen at Agincourt. A lot would be ineffective, but some might find weak spots and cause other problems.)
However such defensive technologies, such as quilted cotton/linen or bronze breastplates, say, are the product of urban civilisation - metal working and diverse crop growing. Just having enough of these specialists to make all the armour for your men would also mean you need surplus food production. Primitive societies just couldn't produce such artefacts for socio-economic reasons. (I will point out that that's probably not quite true, as there have been primitive societies that have on the
very odd occasion been able to equip men in such a manner - but these are societies, when you look into them, that also were producing large food surpluses consistently and thus it was therefore their socio-economic sitatuation again that determined such tecnologies. I am thinking in particular of the American Indians of the Pacfiic coast in the North-west.)
Primitive battles, Keeley argues, were likely to consist of two bands facing off each other, in dispersed formation, at their extremes of bow range, taking pot shots at each other. (If you have no armour and a hit by an arrow will likely cause a wound or death, why present your enemy with a solid scrum of people to aim at?) Melee with clubs, maces, daggers or spears would likely only occur when one side retired/fled and the other came up to finish off any stragglers/wounded. Of course this is about a 'formal' battle where two side present themselves for a fight. A lot of primitive warfare would really be raids and ambushes, so using the element of surprise and more asymmetral.