The thing is, we know how to store nuclear waste in such a way that it's a solved problem forever. Literally gone and not a worry for any generation from now until forever.

It's called deep borehole disposal[0]. Drill a hole all the way down to Earth's crust, put your waste there = it's not coming back on anything shorter than geological timescale. " It is estimated that only 800 boreholes would be sufficient to store the entire existing nuclear waste stockpile of the USA"[0]

From what I understand it isn't being done for two reasons:

1) cost

2) once stored this way it's almost impossible to retrieve. Spent nuclear fuel is kept around partially because we know we might be able to recycle it into fresh fuel in the future. If we dump it in a hole deep in the ground it's gone forever.

[0] https://en.wikipedia.org/wiki/Deep_borehole_disposal