The reason is that the distortion a lens introduces is related to its curvature and aperture.
For a single lens doing the same amount of work as three other lenses, the curvature of the single lens is significantly higher for the same aperture, and the distortion introduced (spherical abberation) is much greater.
Plus, the multiple lens setups may also be corrected for chromatic abberation by using lens elements with different refractive index properties.
Overall, with all else being equal, you generally get better quality from a three-lens setup.
Bill.