Reprocessing is very expensive; $1000/kg and up. Launch to space will likely become much cheaper than this as fully reusable launch vehicles become available. Even if the spent fuel must be armored against accident the cost of launching it to LEO, and then to the moon, is likely to become much cheaper than the cost of reprocessing it here on Earth.

Space disposal has the positive advantage that the seven very long lived fission products are removed from the biosphere, along with the very long lived actinides like Np-237.

https://en.wikipedia.org/wiki/Space_1999