If Tolkien wanted killing Orcs not to be such a problem, then they would have to be without any moral sense, like ordinary animals.
That whole line of thought is deeply flawed and borne out of human hubris as I see it. The fact is that other animals besides ourselves can be argued to demonstrate various forms of morality, such as social-tribal animals for one, such as elephants, the other Great Apes, the domestic dog, parrots and corvids, etc. Observing those animals, you'll routinely see demonstrations of empathy, the sharing of resources, good will and kindness. Mother / young sibling families also demonstrate a degree of morality across a wide range of species, I think.
That said, the general thinking of the time was strikingly lacking when it came to understanding animal behavior, animal intelligence and so forth. So IMO it's not hard to see the hows & whys of Tolkien trapping himself in this kind of pointless dilemma. Plus, along the lines of one scenario, orcs were corrupted elves, first created by Melkor. Where did their morality take a massive hit in that scenario, and did they secretly hate themselves, having a sense of what they once were..?