3DS hardware producer Hideki Konno told Joystiq it's because of that seven-year-old DS screen. "Really, it's all about the backwards compatibility," he said during an E3 interview. "We have to play DS games on this and we want to make sure they work."
Konno said that Nintendo didn't think there was currently sufficient technology to both enable a more feature-rich touchscreen and accurately emulate the touch interface of the legacy DS. "Now that technology may come out sometime in the future, but when we were making our decision on what kind of touchscreen to implement," he said, "that was one of the deciding factors."
That, of course, doesn't explain at all why the Wii U uses the same vintage touchscreen technology. Unless the Wii U is secretly capable of emulating DS games! We're totally onto you, Nintendo.*
*We're probably not actually onto you.