Australia

The crucial, and often ignored, fact is that many people with pedophilia live their entire lives without ever harming a child. You never hear about them because, for obvious reason, they stay in the closet, fearing they will be hated and feared for an attraction they did not choose and have never acted upon. You won't find useful statistics on this, I've looked. It's impossible to collect valid statistics, again for obvious reasons.

Further, not all child sex abusers are pedophiles. Many rapists do so not out of some deprived desperation, but out of a desire for power over another person, a desire to dominate. Children, the elderly, the disabled make great targets for this because they are so vulnerable. And yes, you're right, it is a temptation to have an unsatisfied urge hanging around your neck, as anyone who has tried to give up cigarettes can attest, but it need not be a burden, and people do in fact manage to overcome their urges. There are support groups, there is therapy, and there are safe legal and ethical fictional stories and sexual images (and apparently childlike dolls) which provide outlets that do not require a child to be harmed or an ai to be trained on CSAM for a person to manage their sexual urges.

I repeat, with emphasis, demonizing a safe alternative to actually interfering with a child ironically increases the odds of what you rightly fear. A pedophile is not more likely to rape than anyone else, but any person whose sexuality is repressed is likely to develop some very unhealthy coping mechanisms and a fractured sense of self which can make self-harm and criminal behavior much more likely. Instead of thinking of it as something like feeding an appetite larger and larger meals until it demands a "main course," think instead of a "release valve" providing a control mechanism. Less like handing an alcoholic a beer and then they crave whiskey, and more like giving a smoker a patch to help them manage their urge without acutally smoking. For clarity, yes there are valid addictive concerns here too, I'm not dismissing that entirely.

If it seems like this is a personal issue for me, that's because it is. I was raped as a child, and I have been given more reason than most people to think of how to prevent that from happening to others. From that perspective: I wish my rapist had every available alternative, including a childlike doll, if that's what would have kept him off of me. The critical question in my mind isn't, "will they get bored of the doll," it's "what will they do if they don't have access to something like a doll?"

There, now I've said entirely too much on the subject and am all the way grossed out and want a cigarette.