Such a low rate makes a law problematic:
First, persecution will not be considered as justice, but as an accident.
It increases the danger of blackmail.
It decreases the complicance.
In general, it teaches the involved people that it is possible to violate laws without persecution.
An interesting example of this was the effect of required reports of sexual child abuse for medical workers. The result was simply that pedophiles do not tell their therapists about their experiences or simply don't use therapy. If we assume that there are (at least some or partial) successful therapies, this leads to increasing child abuse instead of helping to fight against.
I think, even in Orwell's 1984 world the rate of detection of pedophile relations will not be much higher. But people which want to establish such a world usually misuse "child protection" as a powerful argument in their fight against freedom.