Your pretend divide between "functional" damage and other kinds is false. No, it's not just aesthetics despite what you claim.
Cut a person's eyes out, and their ghost will usually be blind, stumbling blind through the world and reaching out with clammy hands to search for their killer. Cut their arms off and the ghost will have no arms. Cut a man in half and his ghost will drag itself along the ground by its arms, or possibly fly and strangle people with its trailing guts. Cut their head off and the ghost will have to carry it under their arm (or will have to search for it forever, if you hide it).
Therefore, why should "caving their head in with an axe" not result in a ghost with a damaged sense of self who oozes memories from their rent-open skull and who has impulse-control problems? [1]
Despite the best attempts to pretend "mutilate" means "destroy" - no, it doesn't. Likewise, the attempt to engage in "but muh biology" sophistry and claim that everyone dies from brain damage is likewise at best diversionary.
[1] And despite the pretence that this makes them less threatening, you know, I'd prefer a ghost that remembers more of who they were than one who's lost everything except for how they died and tries to kill anyone they see who has an axe because all they can remember is how they died.
The only people who've been pretending it's childishly simple are the people who've been trying to misrepresent it.
And just FYI? "So, yeah, we systematically mutilate the souls of criminals using thaumaturgical rites where we damage the seat of their soul and quite possibly harm how they interact with the cycle of reincarnation" - which is what a lobotomy would be - means that you're the bad guys. And you're probably turning your jail into a shadowland because you're getting up to some seriously warped shit there.
You know, instead of trying to misrepresent things, could it be possible that the definition of "sophist" is not "disagrees with EarthScorpion"?
And sure it means you're the bad guys, I don't get what your point is there? I say, "It should take a thaumaturgic ritual so that, yes, you're doing it on purpose and yes you should feel bad" you say, "Doing it with a thaumaturgic ritual is bad."
As far as it goes, the question is, what affect do the things you listed with blind ghosts and etc, etc have, mechanically? Like, in each example, you seemed to reject that a person could actually do something without thaumaturgy to meaningfully impair a ghost's ability to fuck you up. You could make their not-life worse, you could change HOW they kill you (flying entrail ghost versus crawling flesh-eater ghost or whatever), but it doesn't seem to really change the fact that there's no real way to assure, via ordinary means, that the guy you killed, no matter how you killed him, will come back to haunt you.
Edit: It just feels, for one, if you make it simply and easily effective (which you seem not to be doing so we aren't disagreeing as much as it seems), that you'd create differences in culture that I'm not sure are supported? As opposed to it being a thing that fucked up magic-users can do (that actually does cripple ghosts), or that is accidentally done in a way that doesn't actually make the ghost less dangerous in any way, shape, or form.
If all you're doing is saying, "Because this ghost was hit in the head (or liver, or whatever) before he died, I decide to move one attribute around to represent poor impulse control" then, again, the vast differences seem to be mostly degrees? Because I'm reasonably sure that Broken25 is not arguing that all ghosts should be exactly the same, mechanically, down to every single stat.