Most toxic elements last forever. That includes the toxic elements in coal ash. Both coal ash and spent nuclear fuel need indefinite safe storage. It can be cheaper to store spent nuclear fuel because it's so much more compact than fossil fuel waste.
Remember that the status quo already has a large forever-waste cost of its own. Nuclear waste is a trade off vs. other kinds of waste, and it is cheaper than the status quo.
Wanted to leap in here to mention tailings from minings projects. The gold that goes into a circuitboard comes from a mine which likely has a tailiings facility and associated dam, which is essentially an open pit filled with water into which tailings are dumped.
They're incredibly toxic materials. We had an engineer go out to the field and take a sample of some tailings, and after 6 months of being left in a lab, the materials had eaten through the stainless steel tube containing the sample.
It's not just power generation that has a negative externality in the form of waste. ALL resource extraction has associated waste.
Not to mention, industrial chemical processes in general.
Toxic waste requiring indefinite safe storage is the default state. Spent nuclear fuel is actually nice here in a way, because in some cases, it's a self-solving problem (dangerous stuff decaying into less dangerous stuff over time).
Remember that the status quo already has a large forever-waste cost of its own. Nuclear waste is a trade off vs. other kinds of waste, and it is cheaper than the status quo.