The "Driver" issues would actually be OS and application related. Let's say that you were to, via whatever method, modify a video card so it supported something ridonkulous like 24 bit grayscale. (Most accurate way I can think of, assuming we're going oldschool and trying to do this with an analog monitor output, would be to make a board that had three very-high-speed 8 bit analog-to-digital converters on one side and a single 24 bit DAC on the other, connected to the single input on a true monochrome monitor. Digitize the incoming RGB signals into three bytes of data, stack them up, and use that on the output side as a single 24 bit value. Easy Peasy, relatively, The simplest method would be to simply use a different value resistor on each RGB line to combine them into one signal; see the comment below as to why from a practical standpoint the results would probably be indistinguishable.) The problem now is that you'll have to describe to the OS that it should treat its 24 bit framebuffer as grayscale, IE, use the three bytes that were RGB into a linear set of luminosity values instead of three sets of luminosity+chroma; if you simply keep working with 24 bit images as 24 bit color you might be able to display some pretty pictures but they won't make a lick of sense if you view them on a normal machine. "Deep Color" support (IE, support for 30/36/48 bit color depths) has been in Windows for a few years but googling seems to indicate it's *not* really in OS X yet. (Oddly there *was* apparently a 30 bit deep color card made by Radius for Macs in the 90's that was supported by PhotoShop.). I have no idea if "Deep Color" support comes along with an understanding of extended grayscale only images, but it would seem to be a prerequisite for really making use of a deeper grayscale framebuffer.
Of course, one thing to think about is if you were doing this analog is the peak-to-peak voltage swing for a VGA (color or grayscale) monitor is only 0.7 volts. Even at 10-bit resolution the difference between two adjacently-shaded grayscale pixels is probably less than the voltage swings you'd get in the cable from, say, ripple from nearby AC feeds or the computer's power supply. 16 or 24 bit would be ludicrous overkill.
That doesn't actually surprise me. 6 bit grey resolution was what Mono VGA was capable of, it would make sense they'd manufacture panels that support it.
I'm sure with the color display the control panel says "256 greys". I would just wager that in practice they're dithered, not true.