The service manager at Tesla informed me that the engineers who analyzed the logs from my car found no anomaly: the TACC performed as designed. The system triggered the emergency alarm when the collision was imminent, and the driver (me) applied the brakes after approximately one second (so much for my catlike reflexes). At the time of the accident TACC was fully functioning: no faulty camera or sensor.
I asked why the car didn't stop on its own--why was I required to slam on the brakes in the first place? The service manager told me that I bore all responsibility. I told him I accepted all responsibility. But the emergency alarm sounded only one second before the time of the collision, I explained, rendering it essentially useless. He repeated that the accident was the driver's responsibility and that he wasn't in the car to witness what happened.
I told him that I didn't remember going that fast at the time of impact (it was a fender-bender after all), and that it seemed like the car should have stopped. It wasn't at all like an emergency braking situation (until the very last second). He told me the accident was my responsibility. I may have sworn at him.
I asked about my speed at the point the emergency alarm went off and he promised to ask the engineers. "We can't know if you were going downhill, if there was ice on the pavement. We can't know any of this," he said. I apologized for being so rude.
I've had time to reflect on this minor accident and I've read all the posts in this string and my conclusion is the following: the accident was entirely my fault. I don't blame the car one iota. I wasn't careful enough and I had unrealistic expectations for the technology. After talking to Tesla, I drove home with my broken nose cone, set the distance to seven, and engaged the AP (my hands hovering above the steering wheel, my foot covering the brake). It worked beautifully.
Thank you for your honesty. It must have been painful to write that post. Hopefully others can learn something from your experience.