Likely because the 2DS has only one screen; the divide that's shown is due to the console's "shell," while underneath, the screen spans top and bottom. I assume it's cheaper to manufacture a device with one screen vs. two. The entire 2DS screen is technically a touchscreen, but (if I understood the articles correctly) touchscreen features are mapped to the "bottom" portion of the screen and effectively disabled on the "display" portion. (As one of the write ups noted, indie game makers could probably circumvent that and possibly create some fascinating stuff.)

tl;dr you can't snap it shut for the same reason you can't snap an iPad in half.