I just realized ABS would be worse in this situation, as if one wheel is turning faster than the others, the car assumes the slower wheels are skidding, so under full power ABS may indeed fail to stop a vehicle. Its one of those situations where the ABS is just plain dumber than the driver.
It is a terrible tragedy. One of the first lessons I give my kids while learning to drive is how to handle a stuck clutch pedal, stuck accelerator, loss of power breaks or power steering, and brake failure.
In the last snow storm I was out blasting drifts with my diesel 4x4, and the fan belt came off. In a diesel this shuts down the vacuum pump so I had no power brakes and no power steering. A wreck waiting to happen. I crept home a couple miles without overheating or wrecking on the icy mountain roads, but stopping a 6500lb vehicle with no power brakes or power steering aint much fun.
Also, older diesels had vacuum actuated fuel shut off. I had a mercedes where the vacuum line cracked going to the fuel shutoff, and the engine would not turn off with the key. There are so many combinations of possibilities, and add panic into that results in a real mess.
Anyone recall the first big news incident where a toyota drove off a cliff in CA killing a bunch of kids? If I recall it was blamed on the floor mat riding up and pinning the accelerator. I wonder now if it was actually caused by the sticking accelerator. I really do find it hard to believe this many people would panic during a stuck accelerator unless there is actually a larger control system failure resulting as described by previous posters that the trans sticks in gear, the ignition shutoff doesn't work, and the ABS of course would counteract panic stopping.
The more I ponder, the more I like my 1992 mazda with power NOTHING. :D