"Just need to solve hills where the driver may need throttle and brake simultaneously to start moving, and it should work."
That problem has already been solved, too. Some manual transmission cars have a "hill start assist" that hold the brakes for a couple seconds to allow easy starts up hills, without rolling backwards. The brakes are released the instant any forward force is detected. It makes starting uphill virtually identical to starting on a level surface. Seems like that should be applicable to auto transmissions as well, which can also roll back a bit before the torque converter locks up.
I like the idea of having a purely mechanical way of removing power to the wheels, which can be done instantaneously in a panic; and that is why I don't trust cars with fewer than 3 pedals!