Do they actually serve a function if they are defined though, or is removing defined organs so deadly only because of the trauma required to remove them. Eg, is removing a liver from a dwarf only dangerous because removing a dwarfs liver requires stabbing them with a sharp piece of metal, or would the dwarf still die even if you just magically removed the organ with dfhack.
It depends on the organ. The lungs, ears, nose, eyes, wings, feet, and brain (maybe a few more, but I think that's most of them) serve a purpose on a creature and that function will be lost if they are removed, but again they don't need to be there to begin with. All the internal organs except guts can't actually be fully removed from a body, but they can be critically damaged which unless they are the brain or both lungs, won't kill a dwarf.
Anyway, this discussion is about game mechanics as they are now, the suggestion was to make the descriptions of violence a bit less graphic I'm guessing, in which case yes it could be done. Though it might have weird effects with modding as mods could add custom organs and such so Toady can't just remove a set list of organs. It would also be a bit annoying the have to add a token to every internal organ that doesn't serve an important gameplay purpose indicating it could be removed. I guess maybe automatically removing every internal organ without a token indicating what it does would work. I'm thinking about it though, and like, it doesn't seem much better without the internal organs. I guess removing the guts body part would probably be good because those do pop out and actually have a tile on the ground behind the dwarf, but like, there's not much difference between "stabs Urist in the lower body with its iron sword, chipping the bone!" and "stabs Urist in the lower body with its iron sword, tearing the pancreas!"