Copper has good heat dissipation capacity but is electrically conductive.
CPU shims should be non-conductive to prevent any accidental short circuiting.
Aluminium shims are often anodized, which makes them non-conductive and improves their appearance (see case modding).
If it is too thick then the heatsink will not make contact with the CPU, resulting in poor cooling and possibly overheating.
CPU shims are nowadays largely obsolete because most modern processors designed for home users since the introduction of the Athlon 64 and Pentium 4 have an Integrated Heat Spreader (IHS) which prevents the CPU core from being accidentally broken.