We had a similar thread a while ago that talked about two-footed driving. The risk with using both feet to drive (specifically, a modern automatic transmission equipped car which I note for the aggravating pedants with nothing useful to add but who insist that the answer account for the peculiarities of the 1892 Humbert Foldabout) is that someone will stomp on both pedals at some point, so a lot of the same issues were discussed.
This is a critical factor. From a stop, stomping on both pedals will allow the brakes to win an easy victory. The car stays stopped, the engine revs and the transmission eventually gets hot. If you did that until the gas ran out, maybe the transmission would overheat and fail first. But the car won’t go anywhere.
In some powerful rear-wheel-drive cars, the rear wheels might spin in place having overcome the resistance of the weaker rear brakes but the stopped front wheels will keep the car generally stopped. The back end might wiggle a bit but the car won’t generally go anywhere until you let up on the brakes. See “brake stand” videos on Youtube.
But, if the car is already moving at speed and you stomp on both pedals (front, rear, or all wheel drive), the brakes may heat up a lot before the car comes to a stop. They may even overheat and become useless while the engine is still racing, generally rendering the car uncontrollable. See my post on the litigation surrounding Ford’s defective cruise control systems, which created exactly the situation of a car moving at highway speeds where the throttle seemingly opened all the way and the driver was left stomping on the brakes to stop it. The short version is that stopping the car was theoretically possible from 5 mph but perhaps not by a weaker driver who couldn’t generate 175 pounds of pedal pressure. The test didn’t start at 75 mph and I suspect the brakes would have failed before the car ever stopped from that speed.
Finally though, modern electronics come to the rescue. Lots of modern cars (but much less than all) will cut the engine power automatically if both the gas and brake are stomped on at the same time and so the car will just come to a sudden stop. No drama at all and nothing broken.