> It turns out I must have fallen sleep in one of the classes when that was explained.

Unless you've studied this at a post-secondary level, I'm afraid that it's quite likely that you've never had it explained to you. My highschool discussed at length the role that the sun, the greenhouse effect, oceans, forests, agriculture, mountain ranges, etc, play on weather and climate, but never actually went through the exercise of energy accounting to determine what keeps the Earth warm.

Which is understandable, because that exercise is non-trivial, and will not actually be convincing to anyone who doesn't have a calculus education.

Radiogenic heating as a primary factor in Earth's heat budget and geologic processes might very well not have even been firmly established when the OP was in school. Alot of what is now confidently taught about Earth's geology and geological history is surprisingly recent compared to other scientific fields. Plate tectonics wasn't firmly established until the 1960s. The Chicxulub impact was highly contentious until the 1990s and not conclusively proven until the 2000s, and AFAIU even today there's still some debate about its role in the Cretaceous extinction, e.g. the interaction with other concurrent events. I wouldn't be surprised if the importance of radiogenic heating wasn't canonical until 1980s, 1990s, or even later and therefore not mentioned in a standard curriculum until Millennials reached high school. I don't remember it being mentioned at all in the 1990s, though re other facts my high school geology and biology textbooks were often many years out of date in some areas--an important and useful coming of age lesson for me, that even academic text books can be and often are sorely antiquated and even outright wrong; and a lesson I might not have learned so early if I hadn't had the advantage of the early Internet.

While radioactive decay plays a significant role in the internal temperature of the Earth, the internal temperature of the Earth plays only a tiny role in the temperature of the surface and atmosphere of the Earth—about 0.03% of the climate energy budget. So for high school geoscience, it’s not worth more than a mention.

Proving the equilibrium requires calculus but simply writing it down doesn't? It's not different from these "water flows into and out of the pool" exercises.