Sure, you could make unauthorized, fully encrypted communication illegal. But what would be the punishment for using it? Worse than for smuggling, human trafficking, murder? I seriously doubt it. If you're a criminal risking decades in prison for major crimes, using some illegal software is 100% worth it, if it significantly reduces the risk of getting caught for the real crimes you're committing.
You can't make laws that govern how criminals behave. All chat control will really accomplish is maybe a momentary string of arrests(which is meaningless in the long term; there's always someone to take over), and longer term, worse privacy and security for everyone except the criminals.