No, economics predicts that _use_ will explode if the cost is zero, but that's not a comment on production.
Pocket cameras have reduced the cost to record sexual abuse, but that's dwarfed by the ability to reproduce/ distribute those copies.
I don't think that means sexual abuse is more common. On every other metric we have, it appears sexual abuse is _less_ common.
Child porn is just leverage to pry. We used to care as much about sending information about birth control through the mail. And with the modern movement to sexualize children as soon as possible, they might have to use another excuse in 20 years. "Terrorism" will always work, because it doesn't mean anything.
The loudness of their voices in "protecting the children" when politicians are introducing new communications surveillance measures, with no mention of local, boots-on-the-ground, child protection services funding increases, just screams to me that they care about surveillance a lot and about protecting children not at all.