Is it really that big of a problem? Sure, the cost of dealing with these is not negligible but in the end, it is just a matter of digging a hole in a deserted place and putting things there. It is dangerous stuff and is to be handled with care, but we deal with dangerous stuff all the times: explosives, toxic chemicals, weapons, ... and nuclear waste is not that high on the list.

The usual argument is that nuclear waste can stay hot for thousands of years. In fact, while true, the kind of stuff that stays radioactive on these time scales tends to be weak, The most concerning elements are usually those with decades-long half lives. Compare to stable but toxic elements like mercury that last forever.

Also worth noting that coal contains long lived radioactive elements that end up in the atmosphere after being burned. So, coal plants also produce nuclear waste, but instead of having it conveniently stored in a specialized facility, it is released in the atmosphere to be stored into your lungs. As I said, long life elements are weak, so it is not that much of a problem, but it is not a reason to do the worst thing that can possibly be done with these.

And while we keep talking about waste, this is only waste because we don't use it. Radioactive "waste" is made of rare elements that produce energy, and maybe a treasure for future generations.