You completely ignored the part where women, children, infants, cattle, sheep, camels and donkeys are to be put to death.
We don't exterminate non combatants such as women, babies, infants and animals. There are clear conducts and conventions in place. There is such a thing as collateral damage but it is avoided as much as possible. In the bible it is the primary goal. Even the animals for some reason are targeted.
Total war is a video game and an oudated concept from bronze age which you seem to still be stuck in.
You still are ignoring the question of what is just in slaughtering infants and animals?
Alright let's talk about that then. Let's think this through logically. Actually let's have another Universe scenario where you are a baby Amalekite and that you are spared. You see in many Years time you will grow up to be a strong man. You will ask your Mother, who was also spared, what happened to your Father. She will name drop the Israelites and in turn you would hate them and want to take revenge. Then you would have all of the other babies who were spared and would go through the same thing. So about 25 Years after the fact the Amalekites would return to attack Israel because they didn't finish the job in the first place.
Did you ever consider that possibility? Look what happened when Hitler made that infamous Dunkirk "Halt Order" command. Britain lived to fight another day. Spoiler, they came back later.
You need to think about these things and not let your emotions take over as the driving force of your decision making.