The REAL problem is the tech monopolies ate the internet. The little sites are still out there, but they are slowly bleeding out to the app/social media giant/google filter bubble monopolies.
I hate to put it like this but the NHS is, largely, unknown to the Americans. They have their own version (e.g.: Department of Health, Surgeon General, etc.) but I think you skimmed on something that is a byproduct of that cultural mentality: Sex and nudity is bad; therefore, any education around that is bad.
People might be able to go and find that information on the NHS' website, if the actual act of doing so wasn't - itself - stigmatised.
There are ripe examples across the internet of people up in arms about sexual education in American schools (this used to be something largely concentrated to the Bible Belt, but as demographics move, has been spreading wider across their country)[0,1].
Then, you have the "think of the children!" crowd.[2, 3]
I think someone paying for advertisement time to say, "If your parents, school, government is failing you, try to look for the information elsewhere - say the NHS," might go a long but - even then - you might be "unpatriotic", "unamerican", "literally the devil", etc. for even doing so.
Fighting the herd mentality isn't without it's own plight.
[0] - https://www.cbsnews.com/news/sex-education-controversy-erupt...
[1] - https://pjmedia.com/parenting/2017/03/31/parents-protest-gra...
[2] - https://www.hli.org/2018/04/comprehensive-sex-education/
[3] - https://www.lifezette.com/2016/12/evil-in-the-classroom-sexu...
Sex and nudity are not bad, porn might be.
There are several researches about it like this one: https://www.psychologytoday.com/us/blog/hero/201603/is-porn-...
Sex !== porn and we should all remember about it.