I think Tolkien, at least in Myths Transformed, very much wanted to view Orcs as irredeemable beings with no real souls, to borrow your description. However, if one acknowledges Orcs as sentient, there's really no way out of the corner he wrote himself into. Tolkien did not think Eru would provide fëar for a race of slave soldiers bound in service to the Devil (HoMe X, p. 410), but once the notion that evil could not create became part of the legendarium, Eru must have been involved in the creation of any sentient beings. "It is not possible to contemplate [Melkor's] absolute perversion of a whole people, or group of peoples, and his making that state hereditable. This latter must (if a fact) be an act of Eru." However, "Eru would not sanction the work of Melkor so as to allow the independence of the Orcs ... unless Orcs were ultimately remediable, or could be amended and 'saved' " (p. 409; emphasis in the original).Voronwë the Faithful wrote: ↑Wed Oct 05, 2022 3:02 amTo me it is pretty clear, particularly if you disregard the "Orcs as beasts" comment in MT that we both don't like, that the Orcs were Elves, Men and/or Maiar that Morgoth has twisted to his evil purpose. The question is whether they are completely unredeemably evil -- as I have argued in the past -- or more victims of Morgoth's evil but still redeemable souls. I am moving towards the latter belief.
This dilemma clearly bothered Tolkien, but it only presents problems if you're invested in the concept of Eru being omnibenevolent, like the Christian God he's based on. I'm not, and in fact I think one can easily point to a number of cases of Eru acting in decidedly non-benevolent ways, so unlike Tolkien, I have no motivation to try to absolve Him of responsibility for the plight of Orcs. The other big objection, as mentioned upthread by Smaug's voice, is that the Orcs being redeemable would cast the Eldar, Edain, and their allies in a bad light, since they tended to treat Orcs as vermin to be exterminated. But Orcs are merely the most horrifying example of the Eldar and the Edain mistreating other sentient beings, not the sole instance: the aforementioned Petty-dwarves and the coastal peoples of the Minhiriath also demand attention.* So on this point, too, I don't think Orkish personhood breaks any essential concepts of the legendarium. I'm actually more bothered by the concept of beings capable of the autonomy displayed by Orcs in LOTR who are constitutionally incapable of making good choices.
* Ditto Tolkien's comment that the Eldar sometimes tortured Orcs and massacred ones who surrendered and asked for mercy, although this was contrary to Eldarin moral teachings (HoMe X, p. 419).