In what car?! All modern mainstream vehicles still use a master cylinder in tandem with a booster and ABS. Even if you lose all engine power, should still be able to apply the brakes. Although it will require more force to push the pedal down, it should still be doable to bring the car to a complete safe stop.
The brakes are never adequate to overcome the power of open throttle. NEVER. One is expected to stop pressing the throttle when applying the brakes, that's why one is taught to use one foot for both functions, so that one does not push both pedals at the same time.
Braking subjects lots of parts to massive thermal changes. Those changes significantly reduce the effectiveness of the brakes after only a small amount of use. That's why race cars and other performance vehicles that are expected to have *ahem* spirited driving have much more expensive brake components, that fade less.
Lastly, look at burnout competitions. In those, someone spins their tires for as long as possible, generating smoke and noise, usually either the longest-burning or the crowd favorite wins. Unless a car has been modified to allow only the non-drive wheels to apply brakes, then the same brakes holding the car still (from a standing stop position mind you, not starting out in-motion) are easily overcame by the drivetrain. Yes, the drive wheels spinning in a burnout competition have their brakes applied and it doesn't do a thing to stop the wheels. Sometimes even the non-drive-wheel brakes are overcome in a burnout competition, and the car crashes into something.
My daily driver is a '95 Impala SS. 260hp, 330lbft torque. Tires are 255mm wide, about 10 inches, and are "W" rated, meaning that they're high-performance for grip and are capable of handling extremely high-speed rotation. On smooth, dry pavement or asphalt it's very hard to do a burnout, the car simply overcomes the brakes and takes off, and that's with probably 75% of the braking force on the front, non-drive wheels. A modern FWD car puts all of its torque into the wheels that would normally do the lion's share of the braking, so once they're overcome, the rear wheels aren't going to do squat to stop the car.
This error is VERY dangerous. The ignition key should ALWAYS overcome the throttle. The brakes should ALWAYS overcome the throttle. The gear shifter should ALWAYS overcome the throttle. Hell, even the four-way hazards should trip the computer into resetting the throttle algorithm.