You're basically trading one regulatory body for another. Perhaps Google makes the "right" decision now, but you disagree with their SEO metrics in the future? We are already beholden to undemocratic tech platforms for a lot of our life, why provide them even more power over our lives? I realize that sounds a little hyperbolic, but it's interesting to see that we are much more comfortable with a multinational corporation that doesn't even have a customer service department to make rules about the Internet rather than a democratically elected government.
Google doesn't publish statistics AFAIK about adult search terms, but evidence from several sources puts adult related search terms at around 10-15% of search volume. Given our metric-obsessed micro-optimization culture, if even a small proportion of those users decided to shift to DuckDuckGo or Bing because they suddenly couldn't search for porn on Google, that would have a material effect on their advertising and bottom line.
I did not propose any rules. I proposed a header.
Google already creates and re-creates "the internet" for the vast majority of people on the regular basis by messing with its algorithm, pre-empting search results with AI-spam, showing ads, etc.
My statement was an assertion that the power google holds over the internet at-large is enough to incentivize compliance with opt-in content ratings for huge amounts of the web.
I also said nothing about adult search terms. The point is that an adult website can mark itself as one intentionally (X-Cotent-Rating: Mature) and then when google gets a search from a child's computer those results are simply filtered out. they already do this but site owners have no way to tell the world their intended audience.