My questions would be: is it possible to improve the visual results if we lift the restriction to only two levels of brightness of each pixel? I.e., would a use of proper grayscale allow creation of smaller fonts that are still readable, or allow more visually distinct and recognizable characters, than a binary font of the same size can have? Would designing a proportional typeface, as opposed to a monospaced one, help with minimizing the average advance width of the glyphs (averaged according to their frequencies in English text)?

Motivation: it is possible to reduce a book page, with ~80 characters per line, without any font hinting, without using any special fonts, using just common image manipulation tools, to just 240 pixels wide, and still get mostly readable words (but not individual letters). This is 3 horizontal pixels per glyph on average, including the gap - something that the demonstrated binary bitmap fonts don't achieve. Example: https://imgur.com/a/AlYrnSS