It's the usual misunderstanding about nuclear waste.
Nuclear waste has 3 components:
- immediately most active and "final" ashes: the fission products: decay time of the order of 300-500 years
- small quantities of unwanted "minor actinides" which could be eliminated in future combustion cycles: decay time of the order of 10 000 years
- plutonium: actual "generated fuel" that is sometimes just left in the waste:
decay time of the order of 100 000 years. In countries with a fuel cycle, this is already extracted (to make MOX).
With decay time, I mean here: the time needed to be of the same (low) activity level as the original raw uranium ore that came out of the mine.
So the strictly necessary and uncompressible decay time to "background" is only of the order of a few centuries.
And now, think about this: how long does it take heavy metals in chemical waste to decay ?