Firstly, do you think a child predator is going to comply with "encryption's illegal you know?"
Secondly, if your imagined case only succeeds because of poor predator opsec, your police are shit, and it's not a good argument for wrecking the security of everyone else in the world.
Allow me to remind you of how Ross Ulbricht, operator of the drugs website The Silk Road, was taken down. Law enforcers infiltrated the site, got chummy with admins and learned more his operations. They seized servers. They did good investigative work to narrow down who the operator was, and when they found him, they surveilled him, and grabbed him in a way that stopped him shutting his laptop, which would have immediately encrypted the contents.
If you hate child predators (and you should), then call for competent police to handle the case and catch them red-handed, don't give me the old "gosh darn it, if only everyone had to go around naked and write postcards, no letters, strip them completely of their privacy. I couldn't solve any cases otherwise!"