On bit restrictions: Also why would bit restriction exclude grays?
Well, look at an example, Amstrad CPC:

You have three possible levels of R,G,B : 0, 127, 255. That gets you 3 pure gray levels : black, midgray, white.
There are a few mildly desaturated colors, like 255 255 127, but these certainly are nowhere near gray. For mixing colors in the way helm is talking about, you need relatively desaturated colors. CPC art mostly avoids creative color mixing for this reason.
As you increase the number of RGB levels, more desaturated colors become available: For example, in EGA64, you have 4 rgb levels: 0, 85, 170, 255.
This gives 4 pure greys plus a few 'sort-of-vaguely-grayish-if-you-squint' colors like 170,170,255.
.. by the time you get up to 16 levels / 4 bpc (Amiga), you have a large choice of hues, 16 pure greys and 30 or so off-grays and can definitely do plenty of blending. The majority of colors available are still relatively saturated, though -- I'd say for example that there is not a 'non-oily' caucasian skin tone in a 444 palette -- you have a choice between rather olive and a bit red in the face.
In addition to what Ptoing explained, it's also rather doable to emulate color restriction, if you have to, via hex #RRGGBB codes.
For example, allowing only one of 00 40 c0 f0 for each channel is equivalent to unstretched ega64 -- 2 bpc. amiga / 4 bpc is also easy to remember, it's just 00 11 22 33 etc up to ff (or #00 10 20...f0 if you're going for unstretched).