What they need is a system where the units have a radial movement distance based three factors. First, a base movement distance based on the units ability to cover a flat distance rapidly. Next, there needs to be a modifier for to the flat movement based on the type of terrain being entered, may that be forest or mountains. Last is, of course, a special modifier applied individual to different units that affect the ability of a unit to traverse a particular type of terrain.
That failing an overlay of circles where the intersections affect costs of movement based on a diminishing return based on the number of all circles present in the intersection.
But for simplicity the squares work just fine. Of course, since Civ is meant to be a game that lets you be in control of everything, and a master of none, Id say its fine.