My terminal emulator has that mapping (because it is designed to be a workalike for kernel terminal emulators that have that mapping). It quite happily supports the other planes. There is no actual fundamental limitation here.

Even with the one-codepoint-per-cell model, what planes one can cover is simply a matter of whether an integer is 16-bit or 24-bit/32-bit. In the Zutty code, it's a 16-bit integer, and I suspect that that is a knock-on effect of the particular way that it flattens fonts out and maps code points to glyph bitmaps, which isn't the only way that one could do that.