I wonder what issues they ran into with using the entire keyboard as a mouse.

I imagine it's uncomfortable to grip since you need to be careful to not press a key doing so. Since you can't rely on fingers much for grip, you could put more force pressing downward with your wrist but that would also add friction with the table. Mice are small enough that you can fit your hand around it, but a keyboard is large and flat.

Put keyboard in perfect ergonomic position on the desk, move mouse, now the keyboard's in a terrible ergonomic position.

Also you have to keep a much bigger area clear for it.

I'm assuming it's too heavy and has too much contact surface (so more friction), making it too hard to glide smoothly.

There's probably something with the position of the hand when you move the mouse as well. At least I seem to be moving mostly the wrist when I use my mouse, meaning that my hand and forearm are not always aligned; without this alignment, I feel there's more strain on the wrist when typing.

I'd also guess fatigue. Pushing around that huge thing constantly

Same, looks like an amazing idea.