The primary process that generates energy in a nuclear reactor, fission, replaces a single atom of uranium or plutonium with two atoms from the middle of the periodic table. These fission remnants tend to be both highly radioactive and chemically toxic, and there is no use for them. They cannot be reprocessed into more nuclear fuel.
These waste products are essential results of the use of fission to generate energy -- you can't get away from them. And they are extremely dangerous. It is also untrue that nobody has ever been harmed by them. The Soviets had an explosion at a processing facility caused by poor storage practices that poisoned hundreds of square kilometers of the landscape around it, well before Chernobyl. These waste products have no value to anybody and it is nearly impossible to get rid of them in a way that we can be sure will never contaminate ground water or otherwise re-emerge into the environment, particularly if we lose the records of where and what they are.
It is also a primary result of the fission process that one atom is replaced by two, and regardless of atomic weight atomic nuclei tend to want to be about the same distance apart in solid matter. This causes the fuel rods to distort as their fuel is burned and replaced by these waste elements, which was a major difficulty for early reactors before this effect was understood. I will grant that this is now understood and generally accounted for in reactor design but it's a thing that took people by surprise. You really don't want to be fucking around with powerful forces that take you by surprise.