Why exclude work related skills? Many of my work-related skill were acquired in Elementary and High School, way way before I ever realized that this is my calling And I do mean not just my job, but my calling; it was simply a calling I resisted for many years. If I’d been able to scootch out of algebra and chemistry because I found them super boring and stupid, I would have had to learn them much later in life, and it would have been so incredibly difficult, just thanks to a lesser neuroplasticity in my brain, that it probably never would have happened. And the world would be short one getting-better-all-the-time-and-someday-will-be-good nurse.
Let’s think of a few of the “basic”, not “advanced” stuff I learned in school:
Basic arithmetic up to algebra and the understanding of how numbers and units relate. I use this every single damn day. My patient is taking one 6mg pill of warfarin. She has a bottle in her closet with a few 1mg pills. Her test came back high and the doctor wants her to start taking only 4.5mg of warfarin a day. If she doesn’t cut back to the appropriate dose, she could risk a life threatening bleeding in her stomach. The pharmacy is closed for the weekend, so they can’t deliver the correct dose. What do I do? (This is not a hypothetical, by the way. This is my yesterday.) The answer is that I give her one half a 6 mg pill and one and one half of the 1mg pills. I need to understand that more pills may not equal more medicine. I need to understand fractions. I need to understand how to get 4.5 out of units of 6 and 1. I don’t use any calculus to do that. I don’t even have a formula for that (although I could figure it out if you put a gun to my head.) I use my understanding of relationships that I got from learning all those stupid formulas and proofs and math facts. That kind of “now it feels intuitive” understanding of math is very difficult to acquire if you’re beginning as an adult learner.
In outside of work life, I like knowing, roughly, what my $63 of groceries will actually cost with tax before I get to the check out, and I like being able to compare interest rates, or the prices across units. Last week, I was at a salad bar which listed their price as 59cents an ounce. Woah, that looks great, right? I mean, I usually pay $5.99 a pound at the other place! 
Language arts/writing/English/composition, I use every day. Exhibit A being this post. (Ooohh…I get to say it: my post is my cite!
) Of course, I also use it every day at work. I have to write a “narrative note,” that will let my nursing supervisor know what the hell I actually did with the patient. That means grammar, vocabulary, spelling…these notes are actually legal documents. If I cannot communicate effectively in them, and someday I’m sitting on the witness stand and can’t answer detailed questions about my patient’s condition and care, I’m, well, fucked. I have to be able to write to communicate with doctors, who often only know what’s happening with their patients when they get my written reports. I have to write instructions to patients that they need to be able to understand without a medical background, so I have to know how to write to different audiences. I have to read with a decent vocabulary to understand other people’s reports, and studies and teaching materials. Had I followed my passions in elementary and high school, this is where you would have found me, up to the hips in books and writing stories.
Gym, nutrition and health: Well, need I go on?
Science, including biology and chemistry obviously, I use at work. Observation and interpretation of data are a huge part of my job. I don’t run a whole lot of labs, but I do spend a lot of time explaining the chemistry of metabolism to diabetic patients, and the chemistry of drug absorption and diet a lot. People don’t remember “don’t drink milk with your iron pill”, but funnily enough they do, if you tell them why with easy to understand chemistry, “Calcium, like in milk, and iron, like in your pill? Well they stick to some of the same receptors in your intestine, so if you drink milk when you take your iron pill, some of that pushy calcium just bumps it out of the way and the iron ends up in your poop. Make 'em take turns - milk with breakfast and iron at lunch, with water.” (And I also have to understand the studies coming out saying that may not actually be the case at all, and decide which way the evidence is leaning and when to change my advice.)
History and social studies: This is the closest to irrelevant to my life. But I do enjoy being able to follow conversations that other people are having. I’m not really sure if I buy the whole, “those who don’t know their history are doomed to repeat it,” thing. Seems to me we do a lot of repeating of very ugly bits of history anyhow. But I do think that humans are wired to be social creatures, and building our social bonds is often best done through discussion of history, recent or distant. That’s what gossiping is, really - recounting recent history to build bonds. Silly chatty monkeys, we are.
What does that leave? Art and Music, I guess. Do I need to know about them in my job? No, not really. But they make life worth living some days. And studies have shown that getting rid of the arts in schools leads to nosediving test scores, increased drop outs and more disciplinary problems, so I’m good with keeping them in the curriculum just on that front.
So…what’s my point? My point is that I think if you dissect most careers, you’ll find a similar smattering of general education knowledge in them. So I think I agree with other posters who have said that high school is *already *pared down to “the basics”. When kids have a passion beyond those basics, those are the ones you see in extra-curricular activities, in band, in theater, in physics club, in student government… Those are the place for self exploration. I’m certainly all for expanding those programs, but budgets don’t seem to allow for it.