But they very much do in Eberron. Khoravar half-elves are a major population block all across Khorvaire and make up two of the Dragonmarked Houses (although one prefers not to identify as Khoravar), and many very specifically reject the notion that they are something less than distinct people unto themselves - they are not humans, they are not elves, they are Khoravar.
Without their own mechanics, there is no distinct Khoravar identity - we can have a discussion about making those mechanics more significant and impactful than previous iterations may have been (I'm not going to pretend the '14 half-elf statblock was especially exciting), but removing them entirely and splitting all Khoravar in the setting down the middle into "really an elf" and "really a human" camps only robs them of the identity they had.
You brought up matters of memories of past lives and the ability to shift gender as possible aspects that help define the sense of elven identity - do those pass on to half-elves that use the elf statblock? Are they denied to half-elves that use the human stat-block? Are any upcoming book authors going to bother asking or answering those questions if all mixed-ancestry characters are shoved into a single sidebar in the PHB from now on?
Tieflings in past editions were (more explicitly) mixed-ancestry characters as well, with both fiendish and mortal blood - should we shoe-horn them into the same mold and make tiefling players choose between using the human mechanics or telling them to go pick out a fiend statblock from the Monster Manual?