Inherent Evil

[Nils]

why would he not allow the Orcs the possibility of redemption when they had no choice in being born as Orcs in the first place?

This assumes of course that Orcs have souls.

In any case, I believe this comment from Morgoth's Ring applies:

The Elves certainly held and taught that fear or ‘spirits’ may grow of their own life (independently of the body), even as they may be hurt and healed, be diminished and renewed.*

*The following was added marginally after the page was written: If they do not sink below a cerain level. Since no fea can be annihilated, reduced to zero or not-existing, it is no[t] clear what is meant. Thus Sauron was said to have fallen below the point of ever recovering, though he had previously recovered. What is probably meant is that a ‘wicked’ spirit becomes fixed in a certain desire or ambition, and if it connot repent then this desire becomes virtually its whole being. But the desire may be wholly beyond the weakness it has fallen to, and it will then be unable to withdraw its attention from the unobtainable desire, even to attend to itself. It will then remain for ever in impotent desire or memory of desire.

Combine that with what I quoted earlier:

It remains therefore terribly possible there was an Elvish strain in the Orcs. These may then even have been mated with beasts (sterile!) - and later Men. Their life-span would be diminished. And dying they would go to Mandos and be held in prison till the End.

If the Orcs had Elven souls, then it would be their inability to repent that would make it that they could not be redeemed.

If the Orcs had Mannish Souls, then I would suppose that they would pass through the Halls of Mandos and join the souls of all Men. I don't remember anything about Men ever having to be redeemed.