they are facilitating the crime to happen in the first place.
Stop being so shortsighted.
There are forums where 14 year old girls talk about twilight. They engage their fantasy online, and lap up any attention they get in these forums.
If a predator comes online pretending to be a 15 year old boy who loves twilight he may fish, and eventually snag, an innocent girl.
The police aren't setting up these chatrooms. They aren't putting real 14 year old girls inside these rooms to attract the flies. They are going into those rooms, and playing the part of the 14 year old girl when they see someone suspicious obviously fishing for the attention of real 14 year old girls.
Yes, they respond in a manner that will give the predator enough rope to hang themselves with, but at any moment the predator has the choice, "Do I talk to this girl about sex, or not. Do I send and request child pornography from this girl or not. Do I invite this girl out or not. Do I meet her and 'help' her live out her twilight fantasy."
It is VERY possible that if the police didn't lay the trap, then the predator would not go through with it - however the police never cross the line of entrapment, which is to say they don't invite the man to do things to them, they simply provide a chatty girl, and respond to his invititations.
For that reason these cases are very difficult to prove in court, entrapment is not a difficult defense, so they are very careful, provide full chat transcripts, and show that the predator methodically and with intent to harm did pursue the 'fake' child, and by so doing they prove that there is beyond reasonable doubt that he committed the crime in question.
Your assertion that if the police were not setting the trap, the predator wouldn't have been successful is faulty - it doesn't matter what he might have done if they weren't there he should NEVER have done it regardless of whether it was a fake girl or real.
-Adam