The desirability of Greek mercenaries in the Archaic period is often cited as an argument in favour of their tactical superiority. The authors you mention are only a few examples of this trend; we could add, for example, J.R. Hale's chapter in Men of Bronze (2013). It is argued that, if other peoples were so keen to hire "men of bronze," as a messenger to pharaoh Psammetichos I allegedly called the Greeks raiding Egypt (Hdt. 2.152), it must be because they offered something that local troops could not provide. The reference to bronze armour is generally taken to imply what that something was: heavy equipment and the related ability to fight in close combat in regular formations.

But the story in Herodotos involves both Greeks and Karians, and he says nothing about their fighting methods. On its own, this doesn't say much about the martial prowess of Greeks at the time. There is no explicit evidence that Psammetichos or any other Near Eastern power specifically wanted to hire Greeks for any reason; they simply appeared on the coast at a convenient time. We can assume that the pharaoh was mostly looking to boost his numbers, and that the Greeks and Karians who practiced piracy along the coasts of the Levant would be eager for more regular employment and a more secure source of income. Herodotos claims that the arrival of the Greeks and Karians fulfilled a prophecy that Psammetichos would be saved by men of bronze, which is far more interesting to him than any tactical matters.

The argument that Luraghi and others have built on the basis of the Amathous Bowl is similarly tenuous. It seems to show men in armour and helmets we associate with Greeks, moving in a regular line and assaulting a city. Again, the mere reference to Greek equipment (and in this case, something like a formation) has been taken as evidence that these are Greeks hired for their tactical skills and superiority to local troops. But how can we be sure?

It would be easier to answer the question if our understanding of Phoenician and Cypriot warfare of the period weren't so murky. We know practically nothing about how these peoples fought. Local descriptions are effectively non-existent and even depictions are rare. On those grounds, it already seems very risky to take one of the rare images from this region and time period and assume that the people depicted on it are not even locals, but Greeks. How would we know the difference?

This is actually where the Greeks themselves come to our aid. Herodotos describes the armour and weapons of all the different contingents in the army of Xerxes. Admittedly it's centuries off, but its claims are pretty striking:

For their equipment, [the Phoenicians] had on their heads helmets very close to the Greek in style; they wore linen breastplates, and carried shields without rims, and javelins (...) The Cyprians furnished a hundred and fifty ships; for their equipment, their kings wore turbans wrapped around their heads, and the people wore tunics, but in all else they were like the Greeks.

-- Hdt. 7.89-90

If we can trust Herodotos here, and if we can assume that Phoenician and Cypriot equipment had changed no more than that of the Greeks themselves in the intervening centuries, then we end up with local people armed and armoured in ways that would be very hard to tell apart from Greeks on a piece like the Amathous Bowl. Their helmets and round shields, the main visible features on the bowl, would look identical at that scale. In other words, we have reason to doubt that the Amathous Bowl even shows Greeks, let alone Greek hoplites in a phalanx formation. We can choose to read it as a depiction of Greek mercenaries in action, but it is perhaps more likely that it simply shows the indigenous warriors and warfare of Phoenicia and Cyprus.

Certainly it is beyond doubt that heavy infantry warfare was known to the peoples of Mesopotamia at this time. The Neo-Assyrian Empire, especially in the 8th century BC, seems to have relied on a corps of heavy spearmen, sometimes depicted with tower shields, to operate alongside its archers and cavalry in battle (for which see Deszö, The Assyrian Army (2012)). There seems to be little need for the Assyrians to hire Greeks if they could raise such troops locally. The Assyrian presence in the Levant means that the Phoenicians had almost certainly encountered these troops and may have adapted their own fighting methods in response; either way, by the time of the Persian conquest they were no strangers to the concept of heavy infantry fighting, as Herodotos' description makes clear.

In this light it seems that the "Greek mercenaries" reading of the Amathous Bowl is putting the cart before the horse. It is assumed that the Greeks had unique value as heavy infantry, and therefore any heavy infantry we see on an object like this bowl must be Greeks. But the Greeks were not alone in using round shields or specialising in close combat. Indeed, they were likely only the westernmost offshoot of a whole range of Eastern Mediterranean peoples (from Egyptians to Phoenicians, Lykians, Lydians, Phrygians and Karians) who mainly fought with shield and spear. The bowl may not show Greeks at all, but even if it does, that may not be because Greeks were at all remarkable - just because they (along with the Karians) populated the mercenary market.

If this is right, then the argument against Van Wees' model of the development of hoplite combat disappears. If we cannot securely identify the men on the bowl as Greeks, we certainly cannot infer that it shows a Greek phalanx in action.

More recently, Paul Bardunias has argued that the formation of closed shieldwalls (akin to a sort of proto-phalanx) is natural behaviour for shield-carrying spearmen behaving as a mob, as each man seeks protection among his peers. Every band of spearmen will almost automatically form a relatively tight formation, however loosely organised, to protect itself from missiles and disruption. This is a more serious challenge to Van Wees' fluid concept of early hoplite fighting, but it still renders the Amathus bowl irrelevant to the discussion; we have no reason to assume that the basic tactics adopted by the Greeks around this time would not be used by similarly equipped Phoenicians and Cypriots as well.