> Edit: looks like it's because BMP supports 1-bit packed pixels and PNG doesn't. The file sizes are almost identical

That's nonsense, PNG supports 1-bit pixels just fine, and the resulting file is a lot smaller (when using ImageMagick):

    $ file unifont-17.0.03.bmp 
    unifont-17.0.03.bmp: PC bitmap, Windows 3.x format, 4128 x 4160 x 1, image size 2146560, resolution 4724 x 4724 px/m, 2 important colors, cbSize 2146622, bits offset 62
    $ magick unifont-17.0.03.bmp unifont-17.0.03.png
    $ file unifont-17.0.03.png 
    unifont-17.0.03.png: PNG image data, 4128 x 4160, 1-bit grayscale, non-interlaced
    $ wc -c unifont-17.0.03.*
    2146622 unifont-17.0.03.bmp
     878350 unifont-17.0.03.png
    3024972 total