The G = 1, loop G, is minimum required to sustain oscillations. G >> 1 is to insure
osc starts up, eg. noise is amped up to get loop going. "Normally" one just seeks G >>1
and doe not modify. There are circuits, AGC, that modify loop G to force G = 1, to insure
amplitude stays constant. Usually used in low distortion sinewave type oscillators.
Typical crystal oscillators don't use AGC, nevertheless requires the oscillation condition unity loop gain in steady state. It's achieved by amplifier nonlinearity. Above a certain input level, the output voltage doesn't increase further.The higher the input voltage, the lower the effective gain.