I agree with the essence of Devdatta Tengshe's answer, except that I believe the main reason for the common use of plane (projected) coordinates over geographic (lat-lon) coordinates is one of computational convenience.
It was and still is very difficult for people or surveyors to do basic CoGo (coordinate geometry) calculations on the sphere (using geographic coords) as compared to doing the same with projected (plane) coordinates.
True, if we do use geographic coordinates as though they were simple plane coordinates, and conduct simple plane computations, then the results are less and less accurate the further away we away from the equator. However, since the use of geographic coordinates pre-dated the invention of cartesian coordinates by thousands of years..., the use of such simple {having difficulty expressing my last point!}(but inaccurate) CoGo methods would not have been possible until cartesian coordinates were invented.