By having more than one anion, many more compounds can be made, and properties tuned to desirable values.
In terms of optics, properties include phosphorescence, photocatalysis, laser damage threshold, refractive index, birefringence, absorption particularly in the ultraviolet or near infrared, non-linearity.
Mechanical properties can include ability to grow a large crystal, ability to form a thin layer, strength, or brittleness.
Thermal properties can include melting point, thermal stability, phase transition temperatures, thermal expansion coefficient.
For electrical properties, electric conductivity, band gap, superconducting transition temperature piezoelectricity, pyroelectricity, ferromagnetism, dielectric constant, charge-density wave transition can be adjusted.