This is pretty cool! It reminds me of that Dragon Ball game that does something similar. Have you considered making a version that uses Mode 0? That way, you could have two standard overlapping parallax layers for each view.
I was recently thinking about how fun it would be to make a Mario-style platformer like that, where each player can completely wander off on their own. The screen would split when they move far enough apart in any direction, and with 2bpp visuals, I think it might even be possible for them to enter entirely different levels—all while staying within VRAM limits for tiles and other resources. With some clever use of row and line scrolling for extra faux parallax, it could look really impressive, too.
Of course, it wouldn’t have to be a Mario-style game—it could just as easily be a run-’n-gun, a horizontal shmup, or something entirely different. Mario was just the first example that came to mind.
Just putting the idea out there. :)