It is - but anyone who thinks that it can be solved right now for all eternity is a fool - all we can do it keep it stable for 500 years (which is doable) and then let our descendants figure it out from there.
We can't assume that advanced civilization will survive another 500 years. There's a whole art project dedicated to the problem of how we communicate to our stone-knives-and-bearskins descendants that the place where we put the nuclear waste is bad and not to be trod on.
I think thats actually a worthy goal, presume the worst, hope for the best. But still, its safe to presume that we have a better than 80% odd of having an advanced civilization still in 100-500 years, when newer, more advanced technology may be able to mitigate to stabilize the problem better. If not, those warning signs for cave men saying "keep away" will probably be helpful. Either way, the costs of continuing to burn fossil fuels is very high - I can't decide if its too high or not - thats for people smarter than I to ponder upon.
Fuel reprocessing can make use of this spent fuel and cycle it back in for more power generation, but the problem here is the processors have a horrendous safety record compared to the plants themselves. They're often trying to squeeze every nickel out of their operations.
If it was a non-profit/federal program that could do things properly you'd have far less material that you had to bury in the desert.