This seems to be demonstrated by this case. They caught the guy through CP but it turns out he actually abused a kid. Maybe he wouldn't have been caught otherwise.
On the other hand is punishing them and throwing them in jail for years actually helpful? As opposed to a lesser sentence or rehabilitation of some kind maybe?
Another problem is that it's incredibly easy to frame people for. Just put some cp on someone's computer or Google account and you can have them sent off to jail with little effort and no way for them to prove they are innocent.