Okay. Glad to know I wasn't misreading you.
So, first of all, your diagnosis of the root problem seems mistaken to me. One of those examples above -- the girl who tried to figure out what century it was a hundred years ago by slightly flawed methodology -- is a clear example of innumeracy, a mathematics fail. Whatever problem is going on in those schools extends to more than just the teaching of humanities.
I don't feel it was mistaken. My diagnosis wasn't meant to specifically deal with each and every issue brought up in the OP ultimately and specifically. But in a general fashion and I think that generally, as I stated in my original post, it was mostly due to haphazard humanities instruction.
In the larger sense, though, I have a feeling would see the dangerous foolhardiness of someone saying to you: "that school system is teaching math poorly, so we should de-emphasize the subject and make it as marginal an elective as we possibly can, since people can go and learn it on their own if they really want to anyway." I don't get the feeling that, as pertains to a subject as important as being able to count, you would fail to see the insanity in that "reasoning." So, I'm puzzled as to why you seem to imagine that the humanities -- which address similarly basic areas of knowledge as being able to synthesize information, comprehend what one is reading and share a reasonably common base of knowledge about society and history with people around you -- are relatively disposable in this way. It seems just completely nuts to me to look at bad humanities education and say not "let's fix it" but "let's throw as much of it out as we possibly can," for much the same reasons that doing this with maths or science would be nuts.
Incorrect. I'd prefer a greater emphasis on the STEM fields, as well as personal finances and English/Grammar/Communications (whatever we can call it) and a base of Civics, as I stated earlier. Reading comprenhension and communication should be covered by Grammar classes, or at least I hope they would, early on. Being able to communicate goes beyond the purview of just the Humanities IMHO and if I misspoke, I apologize. I want people to be able to communicate at a reasonably competent level, or else the STEM education would be useless. But yes, I do find possessing anything more then a basic knowledge of most humanities to be rather disposable unless its in a field one is pursuing or a hobby or passion or something they themselves choose to make an investment in.
I mean, science and maths need partisans, don't get me wrong. I'd be happy to see more scientific literacy and better numeracy in the modern world. But I don't get the kind of partisans who imagine every other sphere of endeavour can be chucked in the process, and fail to see how foolhardy and dangerous that kind of thinking is. When you have schools that don't teach Civics, or teach it as some minimal throwaway subject, the whole concept of citizenship and involvement in democracy deteriorates. When that happens, groups that want to give "equal time" to Creationism in the science classroom -- or teach totally fictional versions of history reframed to make "their side" look more heroic -- gain purchase and power. It's incredible to me that people should fail to see the problem with that.
Civics would be covered, as I stated in my original 'diagnoses.' But I don't see any particular need for expansion of the core curriculum into humanities. They can still exist as electives, both in Secondary School and in College so if people want to invest their time and money into it, they should feel free. But again, I would much prefer an emphasis on a core of STEM + Personal Finances (since many people seem woefully ill equipped at managing money) and as stated before, Grammar/English so they can communicate their ideas effectively. Therefore with this system, there'd be a lot less wiggle room for cultural/societal radicals such as those you bring up, to corrupt schooling. It certainly would be hard to be worse then social studies standards are today. And "theories" like Intelligent Design can be rightfully relegated to the Humanities electives where they belong by an increasingly scientifically literate populace. :)
And again, for emphasis, I don't want to eliminate the Humanities. Just de-emphasize them in core curriculum. Humanities are still important in a broad sense, but individually, I find its importance a fair bit more muted in comparison to learning STEM fields or learning a trade, skill or vocation or how to communicate effectively etc.