It’s going to be hard to find studies which don’t involve CP as most other things have a far smaller criminal significance. They receive less funding as well and it is simpler to extrapolate assumptions from one thing to another. It is also far harder to measure the effects of dolls on crime than CP as there are far fewer dolls than people watching CP, it is too easy for a study to fail to reach statistical significance.
You could try to run a study on a group of people to see if they feel it reduces their desire to have sex with children, however a desire is not the same as a compulsion, or even beyond a compulsion. In fact, a therapy is less about removing desires, than about removing the rejection reaction which causes great distress, and to set up rules about what someone is willing to do. Any rational therapy at least.
In the realm of OCD or anxiety in general, the more obsessed someone is trying to prevent something from being thought, the more they try to resist it, the more they think “I am evil for thinking that”, the more it comes back and turns into an endless nightmare they can never stop. Some level of acceptance is important for reducing it, although someone does need limits on what they’re personally willing to do.
Depending on whether someone is self-accepting and how much so, you may get a different result. And you have to be careful not to include desperate people who may particularly awful reactions to just about anything (likely psychological). Gender dysphoria / mania / hormonal dysfunction may aggravate anxiety. There are a lot of psychopathology to consider and just slapping random people off the street into a study won’t suffice.
Probablistically speaking, it is likely someone who is desperate is going to have more morbidities than something who does not. You may get someone who has mania, psychosis, OCD, gender dysphoria, and who is deeply religious and thinks sex is immoral. It is even worse if someone puts on a show in front of a parole officer.
It is important not to confuse sadism and pedophilia too. When I see dramatic overhyped articles talking about children being tortured and killed, this isn’t really something a normal pedophile would actually want to watch. In fact, it is the very opposite. It doesn’t sound like it is even a pedophile at all and all these weird people get lumped into studies and they assume how they react is how pedophiles react.
Finally, orgasms are very important for a person’s mental health in general, it is well-know to be such. If the alternative is none at all, it is unlikely someone will settle for it. There may be research in that area as it widely mentioned, although I do not know of any. Anything which is deletirious to mental health is going to have a host of negative factors, and these may lead to things which aren’t even related to CSA, but which are equally undesirable to society.
This could mean asexuality could be considered pathological, although it is possible asexual individuals are built differently to alleviate that problem, and if there is nothing they can do about their asexuality, there is little purpose in trying to stigmatize the condition by pathologizing it.