Not to be glib, but the second law of thermodynamics.

You are attempting to filter out trace amounts valuable dopants and some small amounts of metals with value from, essentially, a pile of sand.

This is not energetically or chemically easy.

The second law of thermodynamics is very forgiving here. It's actually not the problem. Energy depends on the log of the concentration.

The problem is with our technology; we don't know how to recycle things well.