It's mostly a United States problem that waste isn't reprocessed. This is now and has been done on an industrial scale in Europe and the U.K. for several decades. For some reason the United States, under the guise of non-proliferation, will not permit reprocessing of spent commercial nuclear reactor fuel.
The story in this article isn't news. Everyone knows how to reprocess spent fuel since before the 1960s. What would be actual "news" is the time at which the United States allows the well-proven, industrial-scale reprocessing to be applied to its own reactors.
Even Canada does it. The United States' nuclear energy policy is laughably stupid. It's a shame, really.