While not having the extra joystick may have been an additional reason, the primary reason normal 3DS couldn’t play New 3ds games was because the New 3ds was significantly more powerful than the original 3ds. For games that only required the extra stick and not the extra power, you could actually just get a grip with the joystick nub and play them just fine.

So, they literally did release a new console, but unlike most makers, they specifically ensured backwards compatibility with multiple generations of their products.