Hmmm, not a particularly enlightening article. Lots of assertions without numbers. How much does reprocessing cost France? How much does MOX fuel cost France to make?
As for the "five percent of nuclear waste, which is composed of long-lived radioactive material" it rather conflates transuranics (with fairly long half lives) and fission products (which are generally fairly short-lived https://en.wikipedia.org/wiki/Long-lived_fission_product#Lon...).
A key benefit of reprocessing is splitting short and long half life materials, which will enable better disposal options tailored to the nature of the material. For instance, short-lived can be vitrified and stored near the surface for a few hundred years, the long-lived baked into synroc. All this has been done.
As for the "five percent of nuclear waste, which is composed of long-lived radioactive material" it rather conflates transuranics (with fairly long half lives) and fission products (which are generally fairly short-lived https://en.wikipedia.org/wiki/Long-lived_fission_product#Lon...). A key benefit of reprocessing is splitting short and long half life materials, which will enable better disposal options tailored to the nature of the material. For instance, short-lived can be vitrified and stored near the surface for a few hundred years, the long-lived baked into synroc. All this has been done.