The new rule is written the way it is for a very simple and obvious reason: It allows you to create a character of any ancestry you like, without having to devise mechanics for splitting up or melding traits from the parent species (which would be a balance headache, take up extra page count, and generally be a pain in the neck).
To say that this is "redolent of the one-drop rule" is preposterous. The one-drop rule is the idea that having one drop of X blood makes you X. In the 1D&D UA, if you have one drop of X, you could be... anything at all. The only rule is that your species traits match those of one of your parents, and it says nothing about which parent.
Uh huh, and I'd say your response is laughable, incredibly high-handed, and fundamentally exactly the kind of "who cares about the message, just think about the page or two a different system might take!" attitude I'm describing.
(This is particularly funny in the context of the 5E D&D rules, which no-one could accuse of making efficient use of page-count.)
And it's very funny that you say "Oh it's not the same because it could be either parent", which is just digging deeper into same fundamental vein of deeply American-style racism. To be clear, this whole "pick one race thing" starts but doesn't end with the one-drop rule. Racial thinking in the US has profoundly been based on "pick one race", "pick one identity" and so on.
It's not really how most of the world thinks, I would suggest, but I guess American exceptionalism leads one to the belief that the American way is obviously superior. You see this culture clash in human rights activism a lot when US activists attempt to export US versions of how things should be without considering that the non-US cultures may not fit well with that (and may in fact be
less oppressive or restrictive in many cases than the US). Even in the UK, a relatively similar culture to the US, it's caused culture clashes with US activists and ideas. It's a complex and nuanced discussion, and perhaps for a different discussion space, but high-handedly dismissing concerns as "preposterous", seemingly primarily on the basis of page-count and apathy seems to me to be profoundly unhelpful and thoughtless as an approach.
Contrast AD&D, in which the rules for human/elf children were laid out in detail: 50% or more elf, you're a half-elf; less than 50%, you're a human; you cannot be an elf if you have one drop of human blood. That is what the one-drop rule looks like in a D&D context, and good riddance.
That's lore that hasn't been valid since, what, 2E at the latest? Sounds more like 1E though. So saying "good riddance" to something we got rid of in either 1989 or 1999 seems a tad fatuous.
From WotC's perspective, really they have a significant risk of getting rid of one problematic element, only to replace it with one that's also very problematic, but in a slightly different way, whilst simultaneously alienating a lot of players.
As an aside, I'd point out that the progressive work in this field in RPGs (and there has been a lot of it, much of it mentioned in this this thread) has absolutely 100% consistently eschewed the "you're only one race really" approach, so any claims that the Origins UA was particularly progressive here are rather obviously refuted by that. Which leaves the only real concern being "But the page count!" (as I've illustrated, D&D's races are not tightly balanced). And
@Dire Bare himself suggested a good solution to the page count issue - which would be an upgraded version of the "custom race" approach from Tasha's. You could easily contain that to one page, one and a half if you were feeling expansive.
Doesn't it seem like it would be fair to allocate the same amount of space to mixed species characters as to just one specific species?