In general U.S. driving students aren't taught anything in the hands-on portion beyond basic handling, turns, lane changes, signaling, parking, etc. In some Euro countries I've heard they even require students to learn to control skids on a skidpad. You'd lose 90% of U.S. students right there.
AWD systems and traction controls systems are two different things, and there are variants of both. The problem with losing power to one wheel in a set when the other slips is inherent to the design of a standard differential, and has existed since long before traction control. It's the reason why limited slip differentials were invented.
Best video tutorial on what a differential does that I've seen is this old one:
http://www.youtube.com/watch?v=K4JhruinbWc
Watch that and it will be pretty obvious why a standard differential tosses all the power at the slipping wheel.
Electronic traction control systems basically cut power when they detect slip. Since most people's remedy for being stuck in the snow is to floor the throttle, it can be a little disconcerting to find that they can no longer do what they shouldn't be doing anyway. I don't like these systems, and I prefer being able to disable them from the driver's seat. The main problem scenario for me is pulling out to cross a busy street with loose gravel under the tires. If I call for power I want power, dammit. I'll worry about slip.