Listing already exists, but in practice it's quite impractical, mainly because it's either not granular enough or too granular.

If the listing feature allows me to allow/deny on a domain basis, then allowing Wikipedia for example would mean that I'd also allow all the non-child-friendly content on there too. Like the literal full-length porn videos or the photographies of genital torture that are on there. And if I block all of Wikipedia, I also block all of the hundreds of thousands of informative and totally child-acceptable pages on there.

If, on the other hand, I allow/deny on a per-page basis, then using the internet becomes nigh unmanageable, because each click of my kid requires me to allow/deny the next page. It's not that often when using the internet that you access the same exact url every day without clicking to sub-pages.

A header would solve that issue. That way I could e.g. allow all Wikipedia articles that are rated for ages 6 and that's ok. The rating should of course be like for movies, so that it doesn't mean that a child would understand the articles, but that there's nothing child-endangering in there like the videos and images (and accompanying texts) mentioned above.