Perhaps half breed would be sterile in certain cases, which is a dilemma, rarely explored in fantasy with half breeds.
The D&D setting called Athas had half-man/half dwarf hybrids called Muls (pronounced like "mules"). Like actual mules, Muls were sterile. Most Muls were created by force breeding to make Muls to fight in the gladiator pits and this usually killed the mother. Though there was a married human/dwarf couple, the mother survived giving birth and they definitely didn't sell their son to slavers.
Fun fact, on Athas Dwarves and Muls are
bald...and proud of it! Basically whatever traits define a Dwarf in any setting, Dwarves are proud of.
Athas had a lot of half-breeds, but they don't go into a lot of depth on the mechanics, culture, and breeding possibilities of much beyond Muls and Half-Elves. Half-Giants are half giant/half human...somehow. The explanation is "magic" but they don't go into details. Most Half-Giants are lackeys to the seven evil sorcerer kings and queens which raises further questions because Giants are not on friendly terms with the sorcerer kings, well they aren't on friendly terms with the one king who lands are near theirs. Athas has also has a weird area infused with some kind of blood magic. Any living creature that bleeds even a little bit starts to mutate, and this area spawns a bunch of new races all the time.
Athas is a rough world. I'm guessing most Athasians would move to the Warhammer world if they could if that tells you anything.
My own WIP fantasy setting, Scarterras. Human, Elves, and Dragons were created by all the gods working together. Every other species represents another god's (or a pair of gods') pet project. Because they have the essence of all nine gods and goddesses, only the aforementioned three are capable of siring or bearing half-breeds.
You reawakened the idea of sterile half-breeds in my head. Maybe I'll use that. Combinations of the Big Three can be fertile but say a half-human/half orc would be sterile....