All the people with money would lobby against content categories because then large mixed category sites like Reddit or Twitter would have to either separate their app, or have the ability to send additional content headers based on content tags per piece of content.

Legally, since pornography still doesn't have a true definition in the US, someone would have to define the categories as well, and then the hundred million free speech fights would begin.

Your vision is the correct one, in my opinion, "adult content" headers would be an easy lift for web technology. But the ad agencies and information agencies (often the same) are spending all of the money to make sure nothing like that happens.