The character ROM was not read and processed by the CPU. The CPU set some bytes in video RAM, which served as indexes into the character ROM by the video output hardware.

I believe on some systems there were some tricks that allowed some bitmap display by redefining glyphs. One example off the top of my head is The 8-Bit Guy's Planet X2, which can use text mode but with glyphs redefined to use for icons, units, terrain, UI, etc.