While I thing we are all in agreement that the real thing should stay illegal, there's actually been studies where cases of sexual abuse of minors INCREASED when real child porn was banned in countries where it is not banned in.
Assuming that it wasn't just a freak thing
It was a freak thing in studies using far too low numbers to be statistically relevant. This is especially important because the studies you mention are methodologically flawed heavily. For instance, they completely ignore that the production of child porn already involved sexual abuse of children. And even when numbers go up, this is usually not because there are more cases (see below)
Real child porn doesn't fall from the sky. Real child porn is created by people raping (and often murdering) real children. These children are victims too, so in any case, real child porn would have to be banned and persecuted. The consumption of (and therefore demand for) child porn creates more sexual abuse of children simply because creating real child porn requires someone raping children, and then spreading evidence of the rape. These children simply are never accounted for in statistics, they are usually living in a different country (with very lax laws, so chance of persecution is low, and thus they are kept out of statistics)
Another thing that there is a gargantuan fallacy in the thought process you mention.
If something is illegal now, and wasn't illegal before, numbers of it being persecuted (and thus found) will often raise. This is painfully obvious: It will usually not be counted before it is illegal. Real child porn being banned usually goes along with awareness for sexual abuse of children, which means that this then raises the number of cases that are reported and persecuted.
A policeman that would, a few years earlier, tell the child to man up and stop lying may now be forced to take the child seriously. Teachers may look closer to the one teacher that keeps going into the girl's dressing room after swimming practice, and react quicker when he takes a girl to his bed during a class trip to "calm her down".
These are real examples, by the way. I remember when these things happened when I was in school. The teacher was infamous among us girls. All classes knew. Fifth years were warned (by students, teachers didn't give a damn) not to go with him into his room because he might undress and photograph you. Parents didn't take it seriously (he was such a "jolly good chap"!), and the school didn't do a thing. I myself complained several times, others did as well. Nothing happened. Nobody cared.
Fifteen years later(!), after dozens of molestations, and hundreds of times he oogled girls dressing, after people talking about this for years, he got arrested. Laws in the meantime had toughened up, the media began to report on cases like this, people were taking complaints seriously. And when the principal of the school changed, and a younger one came into office, he didn't look away when someone complained.
Some people will now go "the law changed, stuff is now really persecuted, and look, the abuse cases went up!"
Sure it did. Because it was completely ignored earlier. Doesn't mean it didn't happen earlier and the law created more cases. The abuses existed before this. It's just that nobody gave a damn.
Why is this case relevant? Well, he was eventually persecuted for the photos he took. It'd be an exemplary case that would show up in a flawed statistic as an additional case discovered after the laws were toughened up.
