"Knowledge of many examined subjects, like languages and maths, is acquired incrementally and cannot easily be crammed into to, say, the last couple of years before university."
You've confused me now. What's special about languages and maths that they should take years? I don't know much about how languages are learned, but common wisdom has it that immersion in a foreign language leads to near-fluency within a couple of years - or have I bought into a myth?
Maths I do know, and I see no reason why it couldn't be crammed into the last few years before university. Here's a story about some American schools where, in the 1930s, arithmetic was dropped entirely from the curriculum up to the age of eleven, with impressive results: www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-schools . I've read a better account of this experiment elsewhere but can't find it at the moment.
From the same author, here are some accounts of children learning maths autonomously, including several who covered years' worth of formal maths in a short space of time: www.psychologytoday.com/blog/freedom-learn/201004/kids-learn-math-easily-when-they-control-their-own-learning
When my dd was nearly ten she was about to start school after being autonomously home educated all her life. She was a bit nervous because people had told her she would be behind in certain subjects, specifically maths. Maths had never been a particular interest of hers and she had never studied it formally. So we bought a workbook intended for her age group, in order to discover any gaps in her knowledge. There weren't any, aside from the odd bit of vocabulary such as "number bonds". Oh, and she was rather hazy about her multiplication tables... but once she got to school she discovered that her classmates were no better at that than she was, despite having been made to practice for years.
At school, I remember that my class spent an entire year learning trigonometry, and not learning it well. My husband learned the same material much better in a few weeks when he needed it for his job as a roofing carpenter. As for me, in the run-up to university I learned a year's worth of calculus in three weeks in order to be allowed to start with the courses I wanted.