In the US it is fairly uncommon (and not required) to find ground fault protection on a typical motor feeder. Solidly-grounded wye systems are most common. When a ground fault occurs at the motor, the equipment grounding conductor (green wire) provides the necessary low impedance path for fault current to flow at sufficient magnitude to trip the phase overcurrent protection. Relying on an external ground connection to a plant grounding grid drastically increases the zero sequence impedance of the circuit, due to the increased inductance. Bonding the motor frame to the ground grid in addition to the equipment grounding conductor will not cause any problems and may provide additional shock hazard protection, but during a ground fault, virtually all of the fault current will flow in the ground wire and not through the ground grid.
The equipment grounding conductor is a legal requirement in the US.