Sorry for the late reply, but for evidence you can look up Robert Miķelsons, who was an active child predator in the Netherlands. He was identified due to images found on a computer in the US. It ended up leading police to him, which caused him to stop. According to further investigations he abused an estimated 83 children, one of which was abused close to 100 times. Many of the victims were less than 5 years old, some were babies.
Without finding the child porn, he would not have been identified and would've victimized many more children.
Surely if one takes measures against only existing material, and not production of new, this only encourages appearance of new material.
For evidence you can look up what happened with synthetic cannabinoids, and how much harm they brought.