Yep a lot of people just completely freeze in emergency situations. They are not sure what to do in the stress of it all, so they end up doing nothing, or doing one thing over and over and over.
Because of this quite a few unintended acceleration events can be attributed to the driver simply mixing up the brake and throttle pedals. Something happens like an obstacle or taping the accelerator while thinking they are on the break, they panic and as the default response slam on the brake pedal as hard as they can...however there foot ends up being above the accelerator pedal. The car starts going faster they panic even more and press the pedal even harder, up until they end up crashing into a wall.
In the event of an bug in the ECU making the car go full throttle can indeed be stopped in a whole range of ways. Like you can turn the key (tho this doesn't directly kill power to everyiyng, ECUs shut down with a delay to have time to safely save data), you can press in the clutch, if you have an automatic you can shift it into neutral. stomping on the brakes hard will bring a car to a stop even if its hurtling down the highway at full throttle...etc But the driver has to think of one of those and do it, yet most people have no idea how a car actually works, so they have no idea what to even do. As far as they are concerned the car is actively trying to kill them and they can't do anything because the car is not acting normal.
Handbrake probably can't stop a engine at full throttle, but even this thing is now electronic. You press a button and a little motor does its whirly business back there to actually apply the 'handbrake'. It is not even a hardwired switch that gives it power directly, it is soft button that tells electronics to do it. Cars also don't have keys anymore, but the ones with a start button typically have a safety feature that it will do an emergency shutdown if you hold the button or press it 3 times quickly or something while the car is on. Id prefer to have the oldschool key and mechanical handbrake.
Because everyone has a car these days, there will always be dumb drivers that do dumb things.