Why is a high value resistor necessary for grounding a MOSFET gate?
Maybe you’re overthinking this.
The diagram you show implies that there is a gate signal connection that is open. Rg is to ensure that the gate has a DC path to source (GND) in the absence of a gate signal. As you noted, this is needed due to the FET gate impedance being practically infinite.
Rg isn’t needed if there’s a ground-referenced gate signal present.