I would really like that actually. I remember fantasizing about this.
First, a high density 3d screen would actually be super impressive to look at, as resolution has big influence on depth perception. I guess (maybe not ?) nowadays, a cheap 1920x1080, being an effective 960x1080 3D
screen would be a possibility. That would be friggin' surreal to see.
Now add what i wold call some kind of 4d tracking. Meaning:
_Gyro in the console changes perspective as the console moves, even slightly, subtly.
_Head tracking changes perspective when your head moves.
That means.. imagine the screen looks like a hole, an empty frame and what's inside looks behind it, independently from how it moves, or you move (of course there is a limit to that in range, obviously). That + 3D, + high resolution, + a 60fps game.. i'm prettttty sure it would melt brains.
That's the kind of thing Nintendo would love. It's doable honestly, all techs are there. it wold certainly be a wayyyyy bigger wow factor than 3D was on 3ds back then. It would basically look real, like it's there.
Also on a different note, but regarding funny visual / gameplay gimmicks. Something i never really see pop out in chats. What if Nintendo plays with super high framerate ? Like.. a 120fps screen with some g-sync equivalent. That would surprise everyone
Anyway what all that means is.. There is a real possibility, with a portable and a custom screen, to have something unique, a visual tour de force than you couldn't reciprocate on any tv in the world. That must be tempting when you create a portable and you're Nintendo..