Not all of it, for sure, but certainly some amount of it. Most perpetrators of child sexual abuse are close to the child, either family members or authority figures (priests, teachers, etc). I expect at least some amount of CSAM originates from these places as well, that the child's parents absolutely had the power (and responsibility) to stop.

Of course, a lot of it comes from major organized crime networks that parents are powerless against. But that then falls under the incidence of more regular police investigations to stop and curtail. You don't need to monitor everyone's chat history to be able to find and dismantle a crime ring.