Of course for this to work the client has to check it and know the device's user is underage. Any devices or software that either do not check or lie about the user's age will be illegal. Since you can write software that does so too, unsigned software that does network access will be made impossible.
That responsibility must move to the parent to ensure young children are using locked down devices that have parental controls and that detect the RTA/adult headers. At that point no third parties are involved and all web platforms must do is add a header to any URL that has the potential for either adult or user contributed content that could become adult and require moderation.