I think it has more to do with the fact that human/elf and human/orc halfbreeds reside in Tolkien, one of the major inspirations for the game.
Given that you can easily just tell your players, "I don't allow half-elves," you need a better reason to remove a traditional piece of the core rules than that some folks don't like them.
The core rules are for basic, general play. I don't like the idea of substituting a race that's far from "generic" fantasy (like githyanki), for something that's rather established in the fantasy genre and a long-time staple of the game. D&D already has enough D&D-isms in it to make them all a bit of a barrier to entry. I'd prefer to not add more.
Most really interesting racial powers (like flight, or teleportation, even if limited) are also powerful. And that becomes a major headache in terms of balance, so again, I'm not terribly interested. And I prefer character powers to be more defined by their choices in life than accident of birth, to be honest.