Your approach—targeting home-schoolers who are “nonconsumers” of public K-12 education—is exactly the approach advocated by disruption theory and specifically the book Disrupting Class. Using public education as analogous to established leaders in other industries, disruption always comes from the outside because the leaders aren’t structurally able to do anything other than serve their consumers with marginal improvements.
ArtofProblemSolving.com is one successful example that’s targeted gifted home-schoolers (and others looking for extracurricular learning) in math. I’m sure there are others. EdSurge.com is a good place to look for existing services, which you can sort by criteria including common core/state-standards aligned (you do have to register for free to get the list of resources). I also have thought about services that build on top of Khan Academy, but I wouldn’t underestimate their ability to improve in that area. They just released a fantastic computer science platform. But they are a non-profit, so their growth depends, I suppose, on Bill Gates’ mood and other philanthropy. To get to full disruption, it might take a for-profit with, as you suggest, monetization through tutoring and other valuable services.
(Similar to Fluttershy) Culturally, there’s a belief that college years are our formative years, and we should be learning to be good, well-rounded (in the liberal arts sense) people. But college is a huge time and money commitment, and the job market is competitive, so I think college ought to be used strategically for advancement in academic or well-paved professional tracks (doctor, lawyer). My college, Harvey Mudd, had a noticeable emphasis on ethics in science and technology and humanities as a hearty side heaping to technical topics. Ideally, ethics would be strategic for career advancement, but in the real world (software engineering), it’s never seem to come up in my job placement. Harvey Mudd should be a pretty good model though since they manage to make it work anyway. Alan Kay also suggested a technical and humanities double major (somewhere in that interview...).
The politics of college aside, here’s my list of things to learn as soon as and by any means possible:
Rationality. Goes without saying here. In particular: using reasoning and empirical data for important questions. I just came across this today that decries the complete lack of empirical basis for programming language design (a topic that’s collectively consumed hundreds of thousands of hours of debate, not to mention time developing mediocre solutions). You’ll see the same thing in any field (at least fields that are mature enough to even ask the question).
Career & finance. Understanding that there’s a game to both and having knowledge about those games can get you opportunities and money that you wouldn’t otherwise. I recommend Ramit Sethi’s material and Tony Robbin’s new book.
Body & brain. You can often get away with research + rationality for a particular question, but it’s good to have prior exposure to solutions to common problems: nutrition/fitness, body language, learning, mental health. For example: thinking “I’m depressed” leads you to: it could be due to a nutritional or neurochemical imbalance, or fixed with changing some thinking habits; instead of “I’m depressed because I’m a failure at life.”
Technical topics. If you want to make a contribution you really need to focus. Math is generally useful, but that’s mostly as a symbolic and visual language rather than any particular deep math topic until you need it. Programming is often useful for automating technical tasks. I’ve observed people who study physics excelling in different topics. (Perhaps exposure to model building and data-driving theory testing. Perhaps selection bias.)
Philosophical and spiritual things. I’ve only started to respect this recently, but I’ve found value in Taoist, Buddhist, Catholic, and Stoic teachings. Here’s someone else exploring a variety of areas.
Microeconomics and game theory come up a lot in the world and knowledge thereof may prevent you from making dumb “If I were in charge...” statements.
Lots of things I wish I knew more about still, like sociology/anthropology, politics, and history, where there’s a lot of “why should I learn about this particular thing or another?” that are hard to answer on my own.