alt Hacker NewsIt's necessary if the page contains mixed content. Under your proposal, Google Search would need a separate search page that shows adult content, and that would be even worse for privacy - logs would show whether you accessed the adult search page - and adult sites (not only porn) would try quite hard to not be relegated to that second, less discoverable, search page.
What you're describing with Google Search already exists, search engines already offer their own search settings including "safe search" or whatever they call it which filters out adult images.
Services can absolutely decide to provide their own content settings. It doesn't require a universal setting or OS requirements, and it doesn't require providing PII to every website or telling a central authority every site you visit.