This is a situation where different people's privacy is in conflict. What's infantile is claiming sole ownership of privacy advocacy while so-whating the worst privacy violation imaginable, from the victims' perspective.
If the median shelf-life of abuse evidence is shortened, in that the item in question can no longer be forwarded/viewed/stored/..., what does that imply in a world where the demand remains relatively stable?
I despise the abusers for what they do, and the ecosystem they enable. But I also remember first having this argument more than ten years ago. If you, as a member of law enforcement or a child wellbeing charity, only flag the awful content but do not do anything else about it, you are - in my mind - guilty of criminal neglect. The ability to add an entry to a database is nothing more than going, "at least nobody else will see that in the future". That does NOTHING to prevent the creation of more such material, and thus implicitly endorses the ongoing abuse and crimes against children.
Every one of these images and videos is a piece of evidence. Of a horrifying crime committed against a child or children.