Would the content rating be per HTML element and the browser would delete the elements with bad ratings from the DOM, or how would it work?

I'd imagine it works like movie ratings. You don't filter movies from scene to scene. There's just one rating for an entire site or app.

But yeah I get the point, API based solutions are complicated and brittle because they require all services to implement it properly. In contrast a user-set app installation password in the OS settings is more effective and easier to implement.