Q:

Why are spherical worlds so rare?

I remember back in the 90s when X-Com came out, being really impressed by the way its world map was an actual world: a map of Earth drawn on a spherical surface.  That was pretty cool, because I had never seen it before.  And now, thinking back... I can't recall just off the top of my head ever seeing it again, with the obvious exception of X-Com: Terror From The Deep, which used the same engine.
Most games that have an entire-planet world map either use a rectangle that wraps around at the sides but not the top and bottom (a cylinder), or a rectangle that wraps around at all four edges (an impossible geometry that some people call a "torus", even though it can't actually represent a real torus.)  And that makes me wonder why.
What difficulties does attempting to build a spherical world map for a video game raise, that it's so incredibly rare to actually see it done?

A:

Because spherical maps, compared to rectangular ones, create a lot of additional complexities regarding the technical implementation and the UI design while usually offering very little gameplay advantage.
First, there is the technical problem. With a rectangular map, you just use a 2-dimensional array to represent map positions. But unfortunately there is no proper way to map a 2-dimensional plane to a 3-dimensional sphere. So if you want your world to be tile-based, then that is usually incompatible with a spherical world (unless you are willing to accept some weird artifacts). And even if your game mechanics are not based on tiles: common tasks which are trivial on a plane, like measuring distances, calculating angles or detecting collisions between geometrical shapes, become a lot more complex when you are doing them in a spherical coordinate system. 
The science of doing geometry on curved surfaces is called Non-Euclidean Geometry. If you want to dive deeper into the mathematical details, then this would be the search term to start your research with. But be warned: It drove various mathematicians crazy for over a millennium.
Then there are the UI problems. There is no good way to show the player the whole globe at once. The player can only see half of the game world at a  time, and everything near the edges becomes distorted. Also, globes are difficult to navigate. If you let the player rotate the globe around the world axis', you encounter gimbal lock around the poles, which results in very awkward controls. If you let the player rotate the globe relative to their viewport, then the globe will end up in strange orientations and the player gets disoriented. A plane is usually far more intuitive for the player.
This UI problem is so prevalent that even real-world applications where it is important to remember that the Earth is round still often decide to visualize the  Earth as a distorted plane instead. Like NASA mission control software, for example.
But dealing with those complications would be worth it if a spherical game world has a notable advantage over a rectangular one. But there are very few game concepts where the shape of the world would make a big difference.
If you wonder if the game you are designing right now should have a truly spherical map or if a planar map would suffice, ask yourself this: Do you have any game-mechanical reason besides "realism" why you want the map to be a sphere? If you can't think of any important game mechanic which would require a sphere and couldn't work on a plane, then do yourself a favor and don't torture yourself with trying to pull this off.

