Upon re-reading your post, Renton, I want to clarify something.

You said, "[...] when a pot of water has just started to boil, the contents are exactly 100 degrees (give or take a smidge)"

This is true the entire duration of the water boiling, regardless of how rapid the boiling, not just at the beginning. The water is 100 C just when it starts to boil, and stays 100 C up to the moment that ALL of the water has evaporated.

Water (pure), in the form of liquid, at 1 atm, can not be hotter than 100 C. The rate of boil does not affect the temperature of the water. A tediously slow simmer is 100 C and a tumultuously rapid boil is 100 C.

***
Now... I have gotten schooled when it comes to cooking. The above is fine for boiling pasta (very close approximation), but when it comes to soups and other dishes, the fact that the water has so much stuff in it changes things a bit.

When there are large chunks of food in the water, they absorb heat and restrict mixing. So the bottom of a large pot is likely hotter than the top. In general, this is not the case with pure water, which mixes rapidly, distributing the heat throughout the fluid.

Not to mention that a rapid boil can pulverize potatoes and other "soft" foods.

I feel like there is more going on in cooking, but I feel comfortable (jokingly) saying that cooking is magic, so clearly not physics.