I feel this is hair-splitting - can't give permission versus informing it's possible.
A DM always decides everything. That's self-evident. In the case of half-elves, but more specifically half-orcs, there was a large assumption about their birth status - I'm pretty sure if you go back, even Tanis in Dragonlance did not come from a loving household.
I'll quote from the new PHB, page 5:
"This is the 2024 version of the fifth edition Player's Handbook. If you've read the 2014, much of this will familiar, since the fundamental rules of the game are the same. But the book contains many new or redesigned elements and the version of things in this book replace versions from older books. Here are highlights: ..."
You can read that however you will choose to, and it seems you'd already made your mind up anyway. To me, that says that, since they're still calling this Fifth Edition, and a revision, that whatever is not SPECIFICALLY overwritten rules-wise still exists. They've always been clear that that is the intent - that essentially they were trying to software-patch something.
Half-elves and half-orcs are still mechanically usable right out of the PHB. The 2014 PHB is still readily available. Half-elves are still in SRD 5.1. I get that people want to clutch at their pearls, and debate what is 2025 RAW, but it's clear to me that half-elves remain every bit 5th Edition RAW in 2025 the same as if this book was merely the PHB 2 like in 4th edition.