I know first hand that my car will not prevent a crash if I press on the gas pedal near an obstacle (that's how I hit my garage wall).

The GP was asking about a scenario of stop and go traffic (if I understood it correctly). I've used autopilot on a couple of occasions on I-5, and indeed, my car stopped when the car ahead did, then it resumed when the car ahead moved forward, maintaining distance and keeping lanes.

It's a different use case from the one you are describing.