Ooh, once we get to "streaming pixel values" out, then we're secretly using the LCD screen's internal memory as a second framebuffer.
The LCD internal memory is write only and it is used just to hold the image being shown. Unlike the GBA where the video RAM is like a GP RAM, just slower.
It is no different than when the atari 2600 used the slow fade of the CRT's phosphor coating as its "framebuffer".
Anything you put out a dedicated video port is gone to you.