Half Orc has lefit historical issues, so Half Elf is dropped by association.
That causing OTHERS (it's it's big tent after all) to feel slighted and so the cycle continues.
Fix the lore.
A thought from above about one way to handle it...
"What some might erroneously describe as apparent cross-species found in published D&D books (centaurs, Dragonborn, etc...) or other possibilities (dwarf-elves, human-orcs, Thri-kreen-dragon-born etc...) are separate species that arose in the ancient past - perhaps naturally (or maybe even more recently) supernaturally, from other planes, or by magic - just like all the ones in the PHB. Rules for constructing balanced abilities for such people to be used as PCs are in the DMG. It also contains examples of how these peoples have unique names not based on their appearances. "
I guess my two questions are:
Does this hurt the settings where there are countries made of half-orcs and half-elves as stand alone races?
How many players using half-elf and half-orc outside of those settings both need it to be explicitly biological and also don't draw on something involving at least one or the other sets of parents people being species-ist?
If the answers are no and not many, then are there any other problems with it?