I understand what you are saying here, and concur to a certain extent. I agree that not every half-elf character's backstory needs to go into the "torn between two worlds" trope. But I think what I'm more getting to is this-- I've seen people thus far talk about how they don't like the removal of half-elves and half-orcs as set races because they now have to just take the mechanics of either human or elf (or human or orc) for their character while saying their character is a half-elf or half-orc. Seems to me that being a half-elf isn't important... the all-important half-elf game mechanics are what are important.
If that's the case and the game mechanics of a race are what matters... then what's the point of having mixed race characters? You could just make more races if players simply want more game mechanic options. Or if you feel like the game needs mixed-race characters, then why are these two the only mixed-race character options in the game? Why are these two so special that they need to be called out when all the other mixed heritages are expected to just be represented by one or the other parent race (other than HE and HO being grandfathered in from editions past?) To me... you either mechanically represent every racial combination by coming up with Multirace rules where a player does indeed pick and choose bits from both parent classes... or you just remove the mechanical differentiation altogether and have players play multiracial characters in their story without needing to give them their own mechanics.
I personally do not believe half-elves and half-orcs need their own independent racial write-up and mechanics while the mul (human/dwarf) and gnoblin (gnome/goblin) and any other parental pairing do not. The game either should go all-in for mechanical representation for every combination, or none at all.
But that's just my opinion, I could be wrong.