There is the problem you describe.And there lies the heart of the problem which no one in this thread is prepared to tackle and provide a direct answer for. People object to child abuse but they are not prepared to give up their privacy. So what's the answer? If the police cannot eavesdrop of conversations held between child abusers which would not only allow them to be captured but also means important evidence can be presented at trial, what is the alternative? Child abusers do use devices that use end to end encryption to they can avoid the police. How do you prevent that?
There appears to be no easy answer but the topic is not supposed to be an easy one either hence why there will be heated arguments on the subject.
Making E2E encryption illegal will not make people not use it. Child abusers will still purchase or download software that offer encrypted messaging, while the rest of us are left unprotected to be exploited for no gain.
Just like with my lock analogy.
If locks are made illegal, criminals will still use locks and risk a small punishment if found out.
And the rest of people will be left with doors unlocked for criminals to enter and steal everything