This wont work because real child sex offenders would never give the key to the FBI. The reason I don't provide a solution is because there isn't a good compromise. However you slice it normal people will end up getting their communications monitored while the real bad actors will be one step ahead. You also can't effectively ban e2e encryption because there will always be a new software that pops up to do it. The end result is always normal people get surveiled and the real criminals are still shielded. That is why I'm saying it's a red herring. They will not be any closer to catching these people by opening up one app to surveillance. Maybe they catch one or two lazy ones but then it will dry up real quick.

If as a layman I had to guess another way to catch them it would be to go to the source. Follow cases of missing children. Investigate reported child abuse. Once you have caught one of them you are free seize their computer and use it to honey pot all their contacts, with e2e encryption so the contacts believe it's person you just caught.