Some early consoles like the NES and the Sega Master had a horizontal screen resolution of 256.
That sounds good for an 8-bit machine, until you consider that a sprite sometimes needs a slightly negative position in order to be partly off the left side of the screen. (Consider e.g. the bad guys in Super Mario Bros, who move onto the screen from the right, and if you and they miss each other, end up moving off the screen to the left.) The upshot is that you need to track an extra bit for sprite positions. Not a huge problem, but it's got to be annoying being so close to being able to track positions in one byte, and just missing the mark.
It would seem that by reducing the resolution to 248, you could represent positions in one byte, without making any discernible change in the quality of the display. Why didn't they do this?