Just consider: If sex work were legal and not stigmatized, there wouldn't be incels, which would rob the far-right of some of its most vigorous supporters.

1. Backdoors in consumer software cannot in fact be restricted to "legitimate" use. All it takes is one "bad apple" to leak the keys -- say, a radicalized police officer leaking them to a fascist group for use in harassing political opponents -- and those keys show up on the darknet and are directly available to abusers. This is a much larger threat than (e.g.) traditional landline telephone wiretapping.
2. If secure communication systems are made illegal, the organizations that build those systems (e.g. Signal) will shut down so as not to be prosecuted for "enabling child abuse". This deprives their current users, including children, of the secure communication systems they are already using today.
3. Sadly, law enforcement officers abuse their power quite often. They also have a higher rate of domestic abuse than the general population. Giving them power to spy on children's communication is directly enabling abusers.

Well. If you put a large glass window on the reinforced steel safe to make sure you can observe inside the safe. You can't exactly expect criminals to not just smash window instantly to take everything instead of struggling to open the safe harder way.

Making master key is also not the approach that works because unlike physical keys, digital keys can be copied millions of times exactly without any flaw over miliseconds without requiring any specialized tool on site.