Case hardening can't increase the tensile strength of the action as the modulus of the case is very near to that of the core. Therefore the core will fail from plastic deformation at the same force with or without the case layer. However, the case layer will be harder and will be more wear resistant; can that be called strength? Also, the higher carbon content will make the case layer more corrosion resistant.

I'm quite sure that the hard layer came before the colors were recognized as "pretty" and desirable. Rub the color layer off and you still have a hard, silver colored, corrosion resistant layer.