In a world where black and white exists, why shoot in color?

Color grabs the viewers attention and makes it much easier for the brain to interpret what it is seeing. There is more imformation in the image than if it is B&W alone. For this reason it is used most often. It is harder to make a popularly accepted image without color.

Not sure I understand the intent of your question, it would make more sense if the question was "in a world of color, why shoot in black and white?"

So I mention why someone would choose one over the other and that should do:

black and white: Originally, it was necessary to shoot black and white because color photography was invented after black and white. But black and white continues to be a popular medium simply because it removes color as a distraction. As art, a black and white image can focus more on the interplay of light and dark, form and function. It gives the photographer the challenge of seeing the world in these terms and trying to capture images that plays on the strengths of having only shades of gray present.

Color: well, the world is in color, and when color phtography became available to the masses, it was vibrant and new - it continues to be the main choice simply because it is how we as humans see the world. As art, photographers choose color over b&w when the color adds to the image, when there's a strong dominant color that will draw the viewer's eye, or if there's a couple of complementary colours that play strongly off each other and so on. In these cases, a color image would probably make a stronger impression than a b&w that removes that feature from the shot.

Color makes your photos come alive and can bring out emotions in the person viewing them that black and white lack. In color, you can show vibrancy and richness and move beyond the composition and form of black and white.

For a person who can produce a good B&W and I mean Good, (like A.Adams) can consider themselves Photographers; it is not that easy.

Ask a 'photographer' if he can shoot B&W, if the answer is "that is out of fashion" or that's obsolete, that persons is not a photographer, simple a SnapShot with the advantage of digital media.