WotC have added clarity by going with species, making it clear there is a major biological division between the different humanoids, they have further made it clear by saying hybrids are because of the magical nature of the D&D universe (not something natural). And to be fair to them ditching half-orcs and half-elves is the way to go if you are making humans a different species than elves.
This does actually put a viable spin on the use of the term "species", and the invalidation of the half- races.
If some cosmological magic is what makes it possible for, say, an elf and a human to have children, but that magic is doing only the bare minimum to make that possible (because the cost at an interplanar scale is horrendous), it is reasonable to suggest that it's merely creating another entity of the same type as one of the parents, and not one that is an actual mixing of the two parents' genetics.
With that world design, half-elves would literally not exist. Humans and elves, being separate species, are not genetically compatible, and do not create hybrid offspring.
Of course that's invalidated by the rule about choosing aspects of one's appearance from either parent, regardless of which mechanical stat block was chosen, which implies there is, in fact, some degree of genetic compatibility. But then there's magic like Alter Self which can do basically the same thing, so again we can blame magic and avoid the genetic question.
It does also bring up interesting (and possibly uncomfortable) questions about the degree to which this magic affects all of the species of the planet. Why only this particular subset of species (ie: the playable races)? If a god creates a new species (race), does it have to register the species with the Cosmological Interbreeding Registry? If it's just "the magical nature of the universe", such a restriction shouldn't exist. Or is that (lack of) limit not written down only as a matter of avoiding "Ewww!" reactions?
Is an owlbear the result of suborning this magic in order to upgrade to an actual genetic hybrid? Is that how the Khoravar came to exist?
As a worldbuilding exercise, this is actually quite interesting. Of course it doesn't solve the problems people have with the characterization side of things.