Low-level waste storage is not really a problem and it can be disposed of safely, plus screening for contamination reduces waste volumes. Waste is designated by potential for contamination and the designation is applied automatically based on a variety of factors, so screening can (and in practice, does) only reduce.
But you're not wrong about the final storage issue for the really spicy stuff. It's a frustrating problem that has been ignored, at least in the US, mostly for politically complex reasons that are difficult to resolve. There are a variety of technical solutions that have largely been ignored while we continue to sit on it; you can legitimately debate the safety and viability of those solutions but they do at least exist and are probably better than what we do presently.
But you're not wrong about the final storage issue for the really spicy stuff. It's a frustrating problem that has been ignored, at least in the US, mostly for politically complex reasons that are difficult to resolve. There are a variety of technical solutions that have largely been ignored while we continue to sit on it; you can legitimately debate the safety and viability of those solutions but they do at least exist and are probably better than what we do presently.