Neither of these things happen, but even if either was miraculously true, should the onus be on the entirety of society to self-censor, or on the kids parents to parent properly (IE use parental controls and supervise screen time)?

Entire society to self censor. Individual parental level controls are ineffective. It’s like keeping your child from having a smart phone at school but then they just become a social pariah since everyone else has one. It only works if no kids are allowed to bring their smartphones to school.