Slight bit of digging around reveals that
the 2DS actually has a single screen covered up to look like two, which kinda makes sense for technical reasons but also is confusing because WHY WOULD YOU COVER UP ALL OF THAT SCREEN SPACE? As Ars points out there's one unsubstantiated but very believable explanation: they were
going for a standalone tablet gaming system, like a Wii U tablet that's not tethered to a console, with the ability to be cross-compatible with the 3DS, and then eventually realized they would essentially be creating a three-way competition between their already floundering touchscreen based systems (and they don't have enough software output to even support the two they have). The tablet design actually makes sense because, if you're going to have a big ol' flat screen anyway, that
would be the right spot to put the buttons (putting them on the bottom would have made it top-heavy). Anyway, so instead of just scrapping the prototypes they decided in their infinite wisdom to slap some plastic bits over the screen, lock it into 3DS mode, and announce that they just made an entry-level 3DS that happens to look goofy as hell. It's... definitely, definitely something that Nintendo would end up doing, historically.
The obvious question at this point is what can be done with it once the plastic's been pried off and a decent homebrew installer's been hacked up. The thing might actually become immensely popular in certain circles.