(Very minor inexpert points on military history, I agree with the overall point there can be various asymmetries, not all of which are good—although, in fairness, I don’t think Scott had intended to make this generalisation.)
1) I think you’re right the German army was considered one of the most effective fighting forces on a ‘man for man’ basis (I recall pretty contemporaneous criticism from allied commanders on facing them in combat, and I think the consensus of military historians is they tended to outfight American, British, and Russian forces until the latest stages of WW2).
2) But it’s not clear how much the Germany owed this performance to fascism:
Other fascist states (i.e. Italy) had much less effective fighting forces.
I understand a lot of the accounts to explain how German army performed so well sound very unstereotypically facist—delegating initiative to junior officers/NCOs rather than unquestioning obedience to authority (IIRC some historical comment was the American army was more stiflingly authoritarian than the German one for most of the war), better ‘human resource’ management of soldiers, combined arms, etc. etc. This might be owed more to Prussian heritage than Hitler’s rise to power.
3) Per others, it is unclear ‘punching above one’s weight’ for saying something is ‘better at violence’. Even if the US had worse infantry, they leveraged their industrial base to give their forces massive material advantages. If the metric for being better at violence is winning in violent contests, the fact the German’s were better at one aspect of this seems to matter little if they lost overall.
Combining the two doesn’t solve the ‘biggest problems of utilitarianism’:
1) We know from Arrhenius’s impossibility theorems you cannot get an axiology which can avoid the repugnant conclusion without incurring other large costs (e.g. violations of transitivity, dependence of irrelevant alternatives). Although you don’t spell out ‘balance utilitarianism’ enough to tell what it violates, we know it—like any other population axiology—will have very large drawbacks.
2) ‘Balance utilitarianism’ seems a long way from the frontier of ethical theories in terms of its persuasiveness as a population ethic.
a) The write-up claims that actions that only actions that increase sum and median wellbeing are good, those that increase one or the other are sub-optimal, and those that decrease both are bad. Yet what if we face choices where we don’t have an option that increases both sum and median welfare (such as Parfit’s ‘mere addition’), and we have to choose between them? How do we balance one against the other? The devil is in these details, and a theory being silent on these cases shouldn’t be counted in its favour.
b) Yet even as it stands we can construct nasty counter-examples to the rule, based on very benign versions of mere addition. Suppose Alice is in her own universe at 10 welfare (benchmark this as a very happy life). She can press button A or button B. Button A boosts her up to 11 welfare. Button B boosts her to 10^100 welfare, and brings into existence 10^100 people at (10-10^-100) welfare (say a life as happy as Alice but with a pinprick). Balance utilitarianism recommends button A (as it increases total and median) as good, but pressing button B as suboptimal. Yet pressing button B is much better for Alice, and also instantiates vast numbers of happy people.
c) The ‘median criterion’ is going to be generally costly, as it is insensitive to changing cardinal levels outside the median person/pair so long as ordering is unchanged (and vice-versa).
d) Median views (like average ones) also incur costs due to their violation of separability. It seems intuitive that the choiceworthiness of our actions shouldn’t depend on whether there is an alien population on Alpha Centauri who are happier/sadder than we are (e.g. if there’s lots of them and they’re happier, any act that brings more humans into existence is ‘suboptimal’ by the lights of balance util).