Very high resistance between gate and ground in MOSFET amplifiers
The resistance you see when you look into the gate of a MOSFET is extremely high, usually several orders of magnitude larger than the gate resistor you refer to. Withouth the gate resistor it will pick up static easily and the charge build up on the gate may easily drive drain-source to conduct or even worse it may build up such high voltages that the metal oxide insulator between gate and drain-source will break down. Once that happens, your transistor is dead.