The reference, in this news item, to radioactive waste is surely misleading; a 'population' of atoms of a radioactive element will disintegrate and emit radiation at their own natural rate whatever we do. A kilogram of plutonium, for example, is not changed in its radioactive properties by being changed into the corresponding amount of plutonium oxide or plutonium anything else (or vice versa). Radioactivity is a wholly intractable property of the atoms concerned whatever their chemical or physical environment or condition. This fact means that any chemical transformation of the radioactive elements in industrial waste is essentially irrelevant to the disposal of that waste. Radioactivity survives chemical change unaltered.
In principle there are but two things you can do with a 'population' of radioactive atoms while they disintegrate and emit in their own natural way: 1) is to concentrate them into a restricted volume, 2) is to disperse them widely. The first generates an intense localised hazard which sooner or later (and the decay can be very slow) will almost certainly escape and spread. The second generates a widesspread 'you never know where it is going to pop up' hazard threatening metabolism, the food chains and the genetic prospects. That is why the 'nuclear waste' problem cannot be solved satisfactorily and that is why the nuclear industry - no matter how safely it may run from day to day - should never have been started and should be phased out worldwide.
I write with some knowledge and much feeling. I am a graduate chemist who, in his younger days, played a very small part in the 'Manhattan Project' and who once helped to propagate the fairy tale that the nuclear industry would be clean, safe and give us electricity 'too cheap to meter'. I have a bad conscience in these connections.