It's not that they perpetuate their own raison d'être, it's that they are addressing path dependent social problems, and changing a system with embedded systemic memory within a vast number of crevices (public, private, and cultural) to hide those memories is orders of magnitude more effort than creating the system at the start.
And yes, I do think that individuals and departments feel threatened that they will be impacted if something like that actually happened.
This applies more directly to something like foster care. My state is going through a budget crisis and anecdatally the result is significantly fewer kids coming into and remaining in care. It moves at the margins so a borderline case that might have resulted in removal before now doesn't.
As you note it's unlikely that some problems can be completely solved. But our resource allocation is mostly fixed or varies based on circumstances beyond whatever problem is being solved.
"75% to 83% of released prisoners are arrested for a new crime" https://bjs.ojp.gov/library/publications/2018-update-prisone...
That's like those stories of LLMs saying "I fixed the vulnerability in your app" by deleting the project entirely