Somehow everyone has forgotten about parental controls that have been apart of consumer grade home routers for years.
Parental controls are there specifically to help parents. These settings allow a parent to block everything online only allowing access to approved lists of websites, generaly done through a whitelist or approved websites.
What is missing at a government level is a curation effort of websites, similar to Libraries that classify books by genres and appropriate age levels.
I would propose a government fund where Librarians or similar organizations can start this effort, and make these lists easily accessible within routers for non tech individuals, together with local initiatives and programs for parents that have a interest to learn more.
For power users lists like these already exists curated by public individuals very similar to pihole block lists and whitelists.
This concept would be the most privacy respectful IMO giving parents the most power to parent, while respecting everyone else's privacy online including children.