Traction control does not "cut power to one wheel". It simply cuts power, and it is way too abrupt for my tastes.
Example, pulling out onto a high speed highway and step down on the throttle to get moving quick due to traffic, if the inside tire spins (we got lots of sand around here), total power cut-off and no acceleration until you completely back off the throttle and start over. Not ideal, to say the least.
Another example, I own some back-woods land with a 1 mile sand (again, lots of sand around here) road. There are some really soft spots and you need momentum to get through. If the tires spin in the sand, the car just quits moving forward. I turn traction control off on that road, too easy to get stuck.
Wish it was more progressive or forgiving.