I'm shocked at how "few" pages printing all 8x8 bitmaps would actually require. Assuming full page coverage of an 8.5 x 11 sheet at 600 dpi I'm only coming with a touch over 548 billion pages. I expected it to be more. Legal-size paper drops that to about 430.5 billion pages.
I think your math is a little off (or maybe mine is).
I'll take a short cut and imagine that you have an 8x8 square with no margins (68% of a borderless 8.5x11), then you have a grid of 600x600 bitmaps, which is 3.6e5. if each pixel is only black or white, than you have 1.8e19 possible bitmaps (64-bit), divide the two and you have 5e13, or about 50 trillion pages. Fix the equation, and you get a grid of 5.2e5, for 30 trillion pages instead of 50.
However, bring that up to 24-bit color or more (even 8-level greyscale is e154), and the exponentiality of the problem goes back to as described by the OP
