Warm water is the waste product because it’s easier dump the water than to cool the water. Returning the warm water to a usable state is much more expensive at scale.

For many microwaves including all of the ones I’ve used, that only lowers the percentage of time the microwave emits radiation. It helps but it still heats the yolk disproportionately in my experience.

Egg yolk cooks disproportionately quickly in the microwave. For runnier yolks, other methods will be closer to desired results.