AFAICT (from watching DummyOS changing colors smoothly enough), the grayscale screen can do 256 shades of gray... or at least, it can do more than 16 shades

The normal 320 x 240 x 4 bpp screen area is stored in SRAM, but the 320 x 240 x 8 bpp area cannot be stored there, it needs to be stored in SDRAM. Upon exit, one has to make sure that the memory is freed and the screen base address pointer is restored, otherwise funny stuff will occur.
And reading from display memory stored in SDRAM might have some unwanted effects (-> critor ?).

The case for hardware 8 bpp mode, on Clickpad & Touchpad, would be to reduce the risk that Clickpad & Touchpad users are left in the cold for SDL-based programs.

Just to give you a quick heads up, the next version--0.2.0--and rather major step, will have numerous changes. Among those will be mouse support, 8 BPP support for CX (thanks to atiatini for the idea; makes it possible to port 8 BPP programs for the CX), many font-related changes (if you're the observing type you can notice one thing on the screenshot below) and a lot of under-the-hood modifications (performance, stability, etc.). Also a few surprises. Quick screenshot to show 16 BPP and palettized 8 BPP on CX (actually it's just an excuse to give the thread some color):

Wow that looks great. When this is available for download, I need to try the color version to see how this looks like on my CX (assuming a demo of the above is made available?).

You'd have to fill the palette RAM with 256 grayscale color values

each from 15 (black) to 0 (white)

However, I think a 256-entry palette mode could still be useful, as nDoom used that even in its original grayscale form.