I very much like your idea of using spreadsheets to model different "savings and loan" arrangements.
I think that playing around with numbers is essential to building intuition. And spreadsheets seem like an excellent way to do that, especially for that kind of problem. And a very natural one that leads directly into work skills.
I think a key thing to learn is the different kinds of families of functions and their qualitative differences, such as linear vs. exponential.
If math is a study of systems, then that includes especially realizing when systems or models break down, when they apply and when they don't apply.
Among my favorite exponential modeling problems are:
I very much like your focus on "why" and your many beautiful examples.
They bring to mind a few more reasons for "why" we have math:
Computers (and all systems) likewise allow us to ignore the underlying meaning. Social software is in a large part a way to avoid human contact by controlling it in very rigid channels.
Joe, my examples are negative, but I think the positive side would be math for citizenship.
I suppose that a distinction can be made between what must be taught-learned and what should be optional. I once thought that what really need to be taught is ethics, what is right and wrong. For example, language should be taught as a way of empathizing with others and ourselves, of caring about them. Math should be taught as the study of systems, especially the systems that we find ourselves in. It's morally essential for citizens in our modern world to distinguish between linear, exponential and periodic behavior and appreciate the implications. Overall, I imagine having a required school of just maybe two hours a day but that focused only on what is agreed to be absolutely essential. Which I think would include drill of "math facts" (multiplication tables, etc.) And most adults as well would be required to regularly show competence. Then the rest of education would all be optional.
About myself: I participated on this list about five years ago. I'm in Lithuania now. I will reintroduce myself but I was moved by Joe's letter and I could not keep from writing my own thoughts. I'm glad to see this list so lively with participants from before and I think new ones as well.