Bestiality. Hear me out.
Orcs are vaguely related to goblinoids (which are themselves fey-ish and more importantly fecund IMC); the goblins kidnap livestock and then some time later there's a true-breeding army of angry, strong, stupid pig-faced (or sheep-faced, or cow-faced) orcs coming down off of the hills to stomp the farmers.
Goblins are naturally generated by dungeons and eat because they wanna, not because they hafta; orcs, not so much, and so form clans or warbands to get the resources they need that aren't supplied by their environment.
They're (a bit) domesticated, letting them swell the armies of local necromancers and warlords; they are mostly-mortal, making them stronger and healthier than their goblin forebears; they're plentiful.
Their priests all have a bit of human blood, somewhere in them. Their warleaders have drunk human blood. It's what lets them break through the 1 hit die barrier
They also nicely side-step the gender issues orcs would otherwise have: there are no female orcs, because they need none; they let other species provide the females. Makes saying "he deals 17 points of damage with his battleaxe!" much easier.
They pair well with minotaurs, dire boar, goblins, and were-beasts; evil mercenary leaders from the ranks of assassins, wizards, evil priests, etc.
And players find their provenance
so distasteful! Not to mention the cultural taboos that the concept of half-orcs brings up.