At this point in time, a 4k screen would be horrible for the GearVR. The current processors simply can't fill that many pixels. The next generation needs to focus on rendering rock-solid 60fps with more polys and less heat. Then when that is under control, we need foveated rendering, which will require support at the GPU and OpenGL level. Then once foveated rendering is working, you can bring in the 4k screens where you render high pixel density directly where your eyeball is looking, and have a lower res rendering for the rest of the 4k pixels, and not cause the entire thing to burst into flames on your face, or run at the speed of a potatoe.
that is not necessarily so. 4k screen doesnt automatically mean that stuff would have to be rendered in actual 4k resolution. you could still render at lower (then interpolated) resolution while still profiting from a giant improvement in regards to screen door effect.