> Two, fission byproducts are both extremely radiologically hazardous and continually producing heat from decay over long periods of time.
It's probably worth pointing out that those two things are the inverse of each other. The elements that take the longest to decay are inherently the least radioactive, because that's what radioactivity is: The consequence of radioactive decay. Something with a half life of 24,000 years is barely radioactive at all. Something with a half life of 24 seconds will give you radiation poisoning very quickly if you encounter a lot of it but won't be anywhere to be found if you come back in an hour.
The waste problem is also largely a political rather than scientific problem. The commonly-cited 24,000 year half life is for Plutonium-239 ("weapons grade plutonium"), which can be mixed at the outset with Plutonium-240 to make it unsuitable for bombs and impossible to separate, and then used as reactor fuel to destroy it entirely.
The most radiologically dangerous fission byproducts (largely Sr-90 and Cs-137) are the ones with ~30 year half lives, making them radioactive enough to cause significant damage and also long-lived enough to persist for several decades, but they also have significant market value in nuclear medicine or radioisotope thermoelectric generators or scientific research.
The massive political stupidity is in not removing the spent fuel from the reactor site and separating it into its constituent elements so that it can be put to productive use rather than sitting around waiting for disaster to strike. And the entire concept of burying it under a mountain for a million years is just ridiculous.