Spent fuel rods can't be used anymore because about 5% of the uranium has been converted into elements that slow down the reaction. The remaining uranium is still good.
Due to a presidential order by Carter, we waste that uranium. The process for recovering the unused uranium (called "reprocessing") is vaguely similar to the process for making bombs. We'd rather not have lots of countries making bombs. The idea was that by not reprocessing our own fuel, we could set an example and hope that somehow that would keep other countries from making bombs. Yes, that is terrible logic.
Japan does the reprocessing. We could do it too, and it wouldn't suddenly arm the world with nukes.
If the fuel is reprocessed, we could cut our need to mine uranium and cut our need to store radioactive material. It's about a 95% reduction. The uranium itself is the long-lived portion, so we'd clear up that problem too.
We could also recover rare-earth elements from the spent fuel. This is the only practical way to create rare-earth elements.
Of course, that doesn't get rid of 100% of the waste. We don't really have a shortage of great places to store it. The worries about burial are blown way out of proportion. All of the proposed facilities for burial are ridiculous overkill.