I'm not sure aluminium is a good example - while your foil is high purity aluminium, large part of Earth is aluminium bound with other elements. Traditionally the main issue was separating it from those.
It's questionable storing all this for later would be more efficient, even with higher purity, than just raffine it from rocks at industrial scale.
Why are you throwing out aluminium foil? Wrap it into a ball, and when the ball gets large enough, put it in the recycling bin.
Analogy: every time I cook using aluminum foil, I cringe at throwing out a usable wad of the metal solely because there's some charred food waste on it, when I presume near-future tech will easily reclaim this useful element. Would be nice to have something between "trash" and "recycling" - pre-sorting junk so that future people have a not-unmanageable repository of materials they can work with even though we can't.
Likewise nuclear "waste" - it's still active material, generating energy, just needing a few more years/decades before we can use it. Even today we have (or soon will) reactors which "eat" waste from older designs. Put what we have in stable long-term containers, and making odds on when it can be used.