The evolutionary answer to this is probably that, while chlorophyll isn't perfect, it works well enough. Along the same line, we might be a lot better off if our eyes could detect infrared light, but we get along fine enough without it.
Chlorophyll is actually quite remarkable in the types of wavelengths it can utilize for energy. Its absorption peaks at both the red end of the spectrum and the blue and violet end. This apparently provides enough energy that there has been no pressure for green light absorption to evolve in this particular pigment.
There are other pigments, though, that can capture other wavelengths of light, including some in the green region of the spectrum. Xanthophyll and the other carotenoids, for example, serve this purpose. However, since chlorophyll captures the remaining wavelengths of visible light, it is basically the star of the show.
Again, it might not necessarily be that reflecting green light is the advantage. Rather, being able to absorb both short wavelengths and long wavelengths of light with the same molecule is enough of an advantage that it outweighs the drawback of not being able to capture the energy in green light.