Why do plants need a variety of pigments to carry out photosynthesis?
Plants tend to carry only one pigment for photosynthesis, which is green and that is the chlorophyll in the plant which is key in the process of photosynthesis.
We see green because that is the part of the spectrum of light which is reflected, which therefore means that the green light is in fact, not being absorbed to produce energy for the plant.
It is however, that green light produces the least energy for a plant during photosynthesis, so plants have evolved to have green chlorophyll, down to the fact that it is that it is more efficient for photosynthesis as it reflects the less productive green light.
Other pigments in plants are also evolutionary, for example that in the flowers, reflects ultraviolet light which certain organisms can see and are attracted to e.g. birds and insects. These organisms help in the reproductive processes of these plants, so the more attractive you can make yourself to a pollinator, the more likely it is that you will have your pollen (basically sperm) flitting about the skies and producing gametes and getting your genes passed on, which is the goal of every organism.
Hope this helps.