Thanks for referring me to this piece of yours. I was inspired by your reading Lord Mahon's Life of Belisarius. I read my fair share of old books, but they tend to be classics of literature and philosophy (or translations of uber-classic histories like Thucydides or Livy) and I've long been meaning to delve into the less well remembered texts of now-obscure historians.
I'm afraid I don't find Ms. Alexander's interpretation, as you've summarized it, convincing. In her telling, Achilles was a kind of proto-John Kerry (recalling his leading involvement as a veteran in the anti-war movement). Tempted though I am, I'll refrain from characterizing it as "projection"--I fear I may have lost all credibility on that line.
Present-day moderns find war to be uniformly awful, for the reason, I think, that war is the negation of the pursuit of pleasure and avoidance of pain which they reckon is the meaning of life, and so war is not only horrid but meaningless. Except, of course, when war is necessary to suppress even worse iterations of anti-hedonistic tendencies than war as such--the atrocities of the Third Reich, for example. War threatens political hedonism, but resolutely ant-hedonist regimes like Sparta or the Third Reich or the Soviet Union threaten it (or can threaten it) even more. It goes without saying that war is horrifying in any of its iterations--ancient, medieval, modern--but regimes and polities that don't orient themselves by the cynosure of pleasure and pain can find a virtuousness in war-fighting that transcends the horror of it.
I won't synopsize Udwin's rival interpretation of the Iliad, except to point out that Achilles doesn't withdraw from the fight out of new-found regret at the horror of war, but rather because of Agamemnon's failure to glorify him as the Achaeans' pre-eminent warrior. It is a traitorous act, whereby he seeks his own vindication precisely by consigning so many of his countrymen to their deaths by his absence. And the responsibility is principally Agamemnon's, who ought to have begun as he needs must end--appeasing his foremost champion.