I did a bit more reading, and found this crazy and scary graph. It's under "Uranium-232 Series Activity" near the bottom of this paper[1]. It shows that gamma ray output from U-238 increases > 5x a year after U-238 is first refined, and stays higher than originally was for >100 years.
It's due to the decay products of U-238 (and their decay products) all producing radiation that adds up to more than the original's.
In fact the base nuclear fuels are almost extraordinarily safer than the products of their use, speaking from a nuclear perspective alone. Nuclear fuel that is stable enough to be useful as a reactor fuel has such a long half-life (usually on the order of billions of years) that it's only very weakly radioactive. But the fission products formed from the fission of the fuel are much much more radioactive.
It's due to the decay products of U-238 (and their decay products) all producing radiation that adds up to more than the original's.
I never would have guessed that.
[1]: http://www.wise-uranium.org/rup.html