There's little practical reason why this couldn't be used for "cultural whatevers", if the system included rules for choosing which benefits the PC got. And there's no practical reason whatsoever such a system couldn't exist in parallel with the "biological" hybrids.
That sounds a lot like the approach to
Culture in Level Up (or A5e), which has already been mentioned.
A5e separates
Culture from
Heritage (i.e., race/species/ancestry) and
Background. Each culture is a bundle of traits that aren't tied to heritage, allowing you to, for example, combine the Deep Dwarf culture with any heritage to represent a non-dwarf who was raised by deep dwarves (or a non-elf raised among high elves, or a non-gnome raised among forest gnomes, etc.).
And since not all of the cultures are based on specific races/species (e.g., there are "descriptive" cultural options like Nomad and Villager), you can go the other way and create an Itinerant Halfling or a Cosmopolitan Orc. Or you could create a character with the Dwarf heritage and the Deep Dwarf culture to really emphasize their "dwarfiness."
It's a neat system... If I ever run any 5th Edition again, I'll definitely be using A5e.