"Some engineer came up with the Wii Remote and they changed everything in the last second."

Where do you get that from? That's not what happened at all. The Wii was a result of a coordinated effort to redefine the user interface and had been in planning stages for years. They spent months refining and iterating on how they wanted their control to work, but the vision of motion control and a pointer were a fundamental part of the Revolution project.

The Wii was certainly luck to some extent, but it was also a calculated move based on a belief that there was a new way to excite ("delight" as Iwata calls it) players in motion/pointer controls and that they should follow that path, despite the competition going with HD graphics over controller innovation.