I just tried saving one of those shade-of-grey "Toner" tile to "4 grey" in xnview, which I guess is a 2bit PNG, meaning it would use 4 shades of grey, so black, white, #555 and #AAA.
The tile went from 32kb to 6kb, so a 80% size reduction.
I'm really curious if this would allow one to store a country region with tiles on a smartphone. OSMand lets you download vector maps to browser them offline, but rendering can be a little slow on some phones.
EDIT: OSM tiles use a 256 colors palette, most tiles less than 10kb. I guess there are tools out there to generate a 8, 16 or 32 colors palette. XNView seems to use libimagequant to generate a palette.