Dorothy Sayers and TLTOL (part four)

These next paragraphs from Sayers' essay call to mind (they are full of questions, after all) far too many examples from my own life and family:

Do you ever find that young people, when they have left school, not only forget most of what they have learnt (that is only to be expected), but forget also, or betray that they have never really known, how to tackle a new subject for themselves? Are you often bothered by coming across grown-up men and women who seem unable to distinguish between a book that is sound, scholarly, and properly documented, and one that is, to any trained eye, very conspicuously none of these things? Or who cannot handle a library catalogue? Or who, when faced with a book of reference, betray a curious inability to extract from it the passages relevant to the particular question which interests them?
Do you often come across people for whom, all their lives, a "subject" remains a "subject," divided by watertight bulkheads from all other "subjects," so that they experience very great difficulty in making an immediate mental connection between let us say, algebra and detective fiction, sewage disposal and the price of salmon--or, more generally, between such spheres of knowledge as philosophy and economics, or chemistry and art?

In connection with the first paragraph, I immediately thought of relatives and friends who think some questionable websites on alternative medicine and sovereign citizenship are correctly informing them.
The second paragraph was illustrated recently. Two days ago, the Washington Post published an opinion piece entitled, "Our Superficial Scholars", discussing Rhodes Scholarship applicants and saying, "high-achieving students seem less able to grapple with issues that require them to think across disciplines or reflect on difficult questions about what matters and why." Isn't it interesting that the high-achieving students, the ones who learned to play and win at the "school game", are now being criticized for not making mental connections between different spheres of study?
I think such compartmentalization is a nearly unavoidable result of our grade 7-12 school structure. When we tell youth that they can only learn math in Algebra (for 53 minutes until the bell rings and they head out the classroom door to traverse the school hallways in a path that cleverly takes them by their latest crush's locker), then world history in World History Class, then music in Music, etc., it is nearly impossible for them in such an environment to see connections between these subjects, especially because they are rarely taught a correlated curriculum that makes apparent the connections between the disciplines.
A great strength of homeschooling is the time and study flexibility to permit children to make inquiries on subjects different from the one at hand. Whatever questions dd6 has about insects or watermelon seedcounts while we read a book about China can be answered quickly (thanks, Google!). Another strength is the ability to teach in a way that promotes making connections; for example, if we have just read a story (language arts) set in a bayou, I can assign a worksheet about Louisiana (geography), read to my daughter about swamp vegetation (biology), and watch The Princess and the Frog (art, jazz, and zydeco).