You don't prioritize the well-being of the other side, but you do want to avoid radicalizing them. The more reasons they have to surrender, the more likely they are to surrender, thus ending the conflict sooner AND keeping the end conditions one they are comfortable living under.
If instead they feel they are in a fight to the death, then you have a much tougher battle on your hand because they will fight to the death. You'll still win (maybe) but it's going to cost you in personelle and time and money.
Next aspect. Moral of your troops. Everyone wants to be a hero, very few people join the military because they want to kill. And those that are in it to kill tend to be toxic leaders which is really bad for the rest of the team.
"Rules of war"/"rules of engagement" are methods that allow your troops to maintain their humanity and sense of purpose under horrific situations. You give up that and you are now undercutting the fighting power of your own forces.
The military did not come up with these ideas to make themselves weak. They came up with them and enforced them because they are the source of strength.