I don't know where you learned about traction control, but the normal way it operates is to apply the brakes on the wheel that's spinning so torque is redirected to the other wheel.
That's how it works in theory and did on some of the first generation systems. In practice most manufacturers cut throttle too (assuming throttle by wire, which most new vehicles have) and you often have to pay for some "off road" trim to get the little button that makes it not cut throttle. On a lot of AWD mom-mobiles you can't even get that option. Also, most traction control systems aren't tuned to hit the brake on the spinning wheel aggressively enough (IMO).
The Episode of Dirt Every Day where he takes a Jeep Compass off roading (it's on youtube somewhere) is a great example of what you can do with good traction control.
