Hmm... Saccadic eye movements typically occur several times per second. I doubt that one's neck can move with such frequency.
In normal vision, saccades are necessary because of the anatomy of the eye. There is a region of the retina called the fovea, where the density of cones peaks sharply. In fact, there are virtually no cones outside the fovea, and the density of rods also falls off as we move away from the fovea. This means, that at any given moment we only see a very small region in the center of the field of view in color and at a high resolution. If you stick out your arm in front of your face, and look at your thumb, your thumbnail would fill your fovea. Everything else is the periphery, which is blurry and gray.
So why do you have the illusion that you always see a vivid picture of the world in full color? Because of the saccades. Your eyes constantly move, and sample the visual field at a high resolution. Multiple fixations produce multiple images which are clear and colorful in the center, and blurry in the periphery. Your visual system integrates these images into a seemingly coherent and vivid view of the world.
Google "change blindness" to see demonstrations of this illusion.