I could do the numerical analysis regarding O'Brien's last point but it's not what I'm interested in.
In addition, I could highlight the ways that O'Brien consistently looks only at armaments prices while ignoring non-armaments military costs that easily exceeded armaments costs - especially in land warfare. But I've already made those points elsewhere.
Rather, I'd like to highlight O'Brien's implicit assumption that, in warfare, price and value are identical or directly correlated. I.e. he implicitly assumes that if a country paid more in Case A than Case B, it therefore has greater military power in Case A. V2 rockets were expensive; V2 rockets were not similarly valuable. Battleships were expensive; battleships were not similarly valuable. Air power was expensive; it doesn't follow that air power was similarly valuable.
The debate over air power's value started before the war ended; scholarly consensus is far from equating its price with its value (Mark Harrison, perhaps the greatest living economic historian of WW2, recently wrote that bombing Germany contributed to victory "wastefully and inefficiently").
Works such as Martin van Creveld's Air Power and Maneuver Warfare document that the Luftwaffe rarely provided close tactical air support in the French Campaign. The Meuse crossing at Sedan is a famous exception enabled by the river's clear demarcation of friend and foe, but here it's now uncontroversial that little physical damage was done. See p.49-50. Even this massive effort caused little physical damage. Van Creveld highlights important interdictions by the LW of French forces attempting to seal the German breakthrough. A full analysis of air power's value (versus price), however, would have to confront the counterfactual: What if instead of so many bombers the Germans had possessed twice as many panzer divisions? In that counterfactual - arguably in reality as well - any French forces successfully moved against the German breakthrough would have been overwhelmed and destroyed. Hitler probably would have felt sufficiently strong to expend armor on an all-out thrust against the Dunkirk pocket, potentially destroying the BEF before its evacuation and possibly turning history on a nightmarish course.
I deeply appreciate O'Brien's analytical approach to how the war was won. Reading it was like having a great conversation with a smart person with whom I disagree. It adds a rigorously quantitative mode of military/economic analysis that is missing from most WW2 and military history. But it's not yet sufficiently quantitative or analytical. Quantitatively, he leaves out the non-armaments factors I've discussed elsewhere. Analytically, he fails to move from the level of price and production to real value on the battlefield.
O'Brien may have in mind an answer to the objection regarding battlefield value. As How the War was Won's opening states: "There were no decisive battles in World War II." The strictly logical reading of this statement is "no single battle was decisive in changing the war's outcome" - a hardly controversial proposition among sophisticated readers. But there's elasticity in the definition of "battle": a sufficiently expansive definition could give us something like "The Battle over Germany" - encompassing the whole Combined Bomber Offensive and German reactions. O'Brien calls the CBO the "war-winning failure." I suspect that some conceptual slippage between "no single decisive (narrowly-defined) battle" and "no single decisive (broadly-defined) battle" has helped O'Brien avoid moving from the production/price level of analysis to the battles/value level of analysis.
Another level of conceptual slippage may inhere in the "how" of his opus's title. "How" the war was won could mean a strictly positive, descriptive account. Obviously the Allies won; this is how it happened. That account would not imply any evaluative statements about the efficiency with which the Allies won, let alone consider whether they could have won more quickly and/or cheaply with other methods.
A different meaning of "how" the war was won implies evaluation - that Allied strategy was broadly correct and efficient - and O'Brien usually sounds in this mode of analysis. The book frequently cites the supposed predominance of air/sea production for all but the Soviet Union (again incorrectly or exaggeratedly, given what O'Brien's narrow armaments focus leaves out). It cites this predominance prescriptively and approvingly:
One of the main purposes of this book is to discuss how the British and
Americans came to engage and destroy the greater part of German and
Japanese production through the application of air and sea power, and
thereby win World War II. It is also to show how air and sea power
combined to keep the results of production away from the battlefield as
well as determining the course of battles (through its action or
absence). By de-emphasizing the importance of land battles, it will pull
the focus of the war away from the Eastern Front (as well as the
fighting in North Africa and Italy). HWwW p.6
The questions I pose regarding LW vs. army value in France apply equally here: were the portions of German production engaged by the Allies as valuable to Germany as what Germany paid for them? Most German aircraft spending was on bombers until late in the war; it's at least very arguable that this was a waste - especially those used against the Western Allies. What is the value of the millions of Germans killed, captured, crippled, and tied down by the Soviet Union? Lacking a WW2 price for military lives, lives don't even get an assumed military value as with weapons (to be clear - I mean military value, O'Brien seems an eminently humane person and I'm not accusing him of callousness).