We criminalize possession and distribution of child pornography on the basis that doing so constitutes further abuse of the child in question.

If we allow the FBI to distribute child pornography, under this rubric we are basically allowing them to commit child abuse. We allow law enforcement to commit some acts -- like buying or attempting to sell illegal drugs -- which would normally be crimes. But we would find acts of actual harm to innocents by law enforcement abhorrent. For example, if an FBI agent posed as a hitman online and then actually committed the contracted murders, that would be abhorrent and not a legitimate law-enforcement use.

Either distributing CP is child abuse or it isn't. If it is, the FBI shouldn't be doing it irrespective of how many criminals they may catch by doing so, because they are further victimizing innocents. If it isn't, that calls into question the basis on which distribution of CP is exempted from First Amendment protection.

Oh wait, I forgot. Different rules apply to those in power.