Dealing with the problem (especially the reprocess part) is not impossible, but it's not trivial, either. After all the colossal transport and storage problems are dealt with (and we're talking about thousands of tons scattered all over the country), the spent fuel elements and their metal birdcages have to be chopped up into little pieces, dissolved in acid, and the resulting slurry chemically separated into its various components. Think of a major oil refinery run entirely by remote control.

Then each radioisotope must be disposed of separately, depending on its final volume (most of it will still be in acid solution), concentration, lethality and half-life. The most dangerous wastes can then be vitrified into compact bundles for permanent storage. And this must all be done behind walls, with waldoes, because the stuff is so dangerous. This is not scientifically impossible, but I don't think its been done anywhere on an industrial scale. As you can imagine, it will be dangerous, and expensive. I don't think the industry can afford it, which is why they always passed the buck to the government. If it had been easy, it would have already been done. The French have supposedly done it, but I don't know how their system works. In fact, I can't imagine how.

Not that we have any choice. Even if nukes are abandoned today, the stuff already exists. I think this is the nightmare waiting to happen, not a meltdown, leak or explosion.