That's much harder to implement. If you ban advertising eg. online casinos to underge users, the service would have to send two different ads (one 18+ and one for younger people too), and the browser would have to decide which one to play. Same for eg searching on google, browsers would have to filter out every <div> with adult content, meaning half the page would be empty, but with a browser "underage" flag, google could just turn on safe search and not allow turning it off.
Plus, as soon as the user clicks on one of these optionally filtered elements, the service will know how exactly what browser is filtering.