The prohibition against killing is specifically innocent people.
OK, that makes more sense.
were usually either to reclaim parts of Israel which belonged to them from the gentile nations that were inhabiting them
Seems like a flimsy excuse to slaughter babies. Though I suppose the Amalekite case can be somewhat justified by an uncharacteristically utilitarian calculation on God's part if Amalekites presented an x-risk to Hebrews. But that is not how the issue is usually presented.
From your link:
The Brisker Rav inferred that this indicates that they did not accept the seven mitzvos or terms for peace (both of which are necessary criteria according to the Kesef Mishne's interpretation of the Rambam1), otherwise they would not have been called "sinners"
...so they wiped out every woman and child? In any case, this inference seems like an extreme case of motivated cognition: "what we did was right, therefore they must have done something wrong even if we have no records of what they did". Further reading of your links provides a fascinating insight into how far this motivated cognition can lead otherwise very smart people.
That it is indeed a case of motivated cognition can be trivially shown by transplanting the question into a modern setting and asking under which circumstances it would be ok to wipe out a whole people today. The answer is clearly "none" (I hope). Yet what (ostensibly) happened then has to be justified at any cost, or admit that Saul and Samuel were little better than Hitler and Pol Pot. Or that human ethics has evolved and what was acceptable back then is a high crime now.
Eh, I take back the unnecessarily emotionally charged reference to the iconic supervillains.
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