I mean you're just making a different oversimplification to me, you're not really shedding any additional light.
The point is, the Greeks clearly recognised a bad "war" god and non-bad "strategy/victory/discipline" god.
Absolutely not, and that's not a reasonable position, nor supported by history. Indeed I would go so far as to say it is illustrative of a profound misunderstanding of ancient and classical Greek culture. This isn't about "PR". This was about different concepts, ideas, and ideals being associated with each.
Good thing I didn't say that, eh?
I said the a lot of cultures recognised that war was not a good thing, or certainly high-intensity war.
EDIT - I will add that the few cultures I can think of which did have positive "war gods" were ones which rather troubling cultures which engaged in large-scale and frequent acts of "Evil" by D&D's standards. By D&D's standards for, example, most eras of Rome's existence are of a very clearly Evil-with-a-capital-e society. Your objection seems to be more that D&D has/had capital-e Evil and capital-g Good at all.