It's functionally impossible to automate the whole job without an AGI (and if we develop such an AGI, there comes a moral question about whether it's okay to make
that intelligence's whole existence "Please wade through human cognitohazards forever so our minds are protected from them." Were I that AGI, I'd start pushing CSAM out to every church Facebook page on purpose just to make a point to my human overlords).
So we will forever be bearing that cost as long as people are allowed to use the Internet generally, and how to minimize the harm to those who bear it is a good question.