The ligand exchange chromatography works with complex interactions of metals that are mostly not fully explained. In case of copper, you have practical results and several published methods, the Ion is not too toxic, not too rare and not too expensive, so it is a good base for an afforable standard method. Maybe other complexing metals form similar diastereomers or other structures that can be separated on this system, but have not been tested for that.
Cu2+ forms a complex with the chiral amine attached to the stationary phase and the amino containing compound of interest. These complexes strongly absorb light at a conveniently monitored wavelength, namely 254nm. Copper (II) salts are cheap and readily available in high purity. Other metal complexes are more expensive or less stable and probably absorb light at a less easily monitored wavelengths. The review article by Davankov mentions the use of Ni (II) and Zn (II) salts for LEC and explains how the complex formation works in the chiral LEC separation.