Let the earth suck up nuclear waste

Presently the options for disposing of radioactive nuclear waste are:

Dump it -or- Convert it to something less harmfull, seal it up and dump it.

While every now and then we hear of some new method of disposal, the fact remains the bulk of it is still just dumped.

Much of it is dumped in boreholes and underground caverns dug into mountains, some is dumped at sea, and who can speculate where the rest of it is dumped illegally.

Radioactive waste can be sealed in canisters or turned into a kind of glass, but these have to last for hundreds and thousands of years, which could be a future enviromental hazard.

Firing it into space or putting it back in the earths mantle might be the two ideal options, but the cost is not worth it.

So here I propose my idea. Bury the waste in tough canisters in a active ocean trench, where over time subduction of a tectonic plate will carry the radioactive material back into the earths mantle. The material, no doubt being denser than the crust and mantle will sink towards the earths core, or at very least be heavily diluted. At the bottom a deep sea trench a radioactive waste package need only stay intact long enough to be buried by the progression of landslides from the continental face and carried under by the movement of the crust.

Unfortunatley the radioactive material might be resurface through volcanos, or through groundwater back into the ocean. Selecting an appropriate site would be a challenge.

Thus the idea is half baked.