My T-bird used just the rear brakes to slow down the spinning tire/s. My manual warned that if the traction control got activated frequently, it would shut down if the brakes got to hard. It would resume, once things cooled back down. I can't say that I ever ran into that though. I did not like they system since the brakes would oftentimes slow my tires down to the point where they would stop completely. I drove it to a NASCAR race in Martinsville one year right after a weeks worth of rain and floods. I parked in the grass on a slight hill. While I stepped on the gas, all I got was the "whirring" of the TC and my tires planted on the wet grass. Several people saw what was happening and gave me a push to get me going. I'm not thrilled with that type of TC. I'm sure that if I would have floored it, it would have overcame the pressure from the brakes, but I never tried flooring it when the TC kicked in. Kinda defeats the purpose in my mind.
I also agree with your comlaint about the systems that limit the throttle in addition to the brakes. I rented a '00 Mustang last year and ran into the same situation. I was pulling out off of a gravel road onto an asphalt road. I took off a little to aggresively, so my rear tires broke free. There I was sitting in the middle of the road with traffic coming up behind very quickly. An ideal system would sense the regain of traction quicker and shut off the TC sooner. My T-bird would disable quicker, however it suffered when it came to getting going when it was really slippery.
My Explorer blows away everything else I have ever driven when it comes to taking off. It acts similar to a system that limits the power to the rear wheels. The difference being that instead of just cutting the power, it redirects it to the front. So instead of sitting their dead in the street, it takes right off.