I think it's problematic because they're presented as core races for...some reason. They don't have any history as societies, which makes perfect sense for the reasons you gave, yet they're somehow common enough to be deemed as worth putting into the player's handbook. Sure we have tieflings in the handbook too, but they're explicitly born from supernatural circumstances and are entirely unique entities as a result. With half orcs and half-elves, they're really just people. Why aren't there half-dwarves or half-gnomes included? And why aren't there half elf, half-dwarves? Or half dwarf, half-orcs? That's where the issue arises. It's not the biggest issue in my opinion, but I think having mechanics to make any combination of half-breed rather than specific ones is the better way to go, just to put my two cents on the issue.
