There's more than saving vram. Graphic cards support textures only up to a specific size. Modern cards may support 8192x8192, older may only support 512x512 or even only 256x256.
So, when you have a huge image, let's say 8192x4096, you should cut it into smaller pieces, if you want to support players with older gfx cards.
Also, when using pixel shaders in your game, you could get in trouble, too. Only ps3 (and up) is guaranteed to work on 4k textures. (This could be misleading, let me say it this way: If a card supports ps3, it also has to support 4k textures)
But you could also still save some vram. Let's take the example 800x800. It's just a matter of how you split the image. See the graphic below: