It would make the microphone half-off, still capturing the upper half of the soundwaves.

No, the output of electret capsules is generally wired as a common source amplifier at Ugs ~0 V with an N-JFET. Without bias, there will be neglibible output (~essentially only the capacitive coupling from the gate to the output; if you SPDT the bias voltage to ground, you're having a >100 MOhm source impedance (the capsule) fighting a couple kOhms (bias + input resistance) through perhaps 5 pF or so.

Yes, but then we're back to loud popping sounds when you turn it back on.

You could ramp up/down the voltage gradually.

Anyway the thing is connected to an ADC. The computer can sense when the switch is turned on/off, and turn off (or flush) the audio pipeline at the appropriate times.

How does the ADC distinguish the transient from switching the bias voltage from an intentional signal? (Yes, if you see the entire waveform, this is quite easy, but because of the low frequency, this would incur another ~20-50 ms in latency, which is unacceptable).

Ramping the bias voltage requires additional components (cheapest way these days would probably be a separate DAC integrated into the audio codec, but then you are back to not having a physical kill switch) and also incurs extra delay for turning off and on (probably 100-200 ms).