Iirc hdmi has 19 wires. USB c is around 10 (but mirrored so ~20 on the connector). Making hdmi symetrical would require a 38 wire connector which would be large and prohibitively expensive.
USB-C uses 24 pins if you use the same criteria you're using for HDMI. Making HDMI symmetrical would be simple, albeit a connector redesign. USB-C already has the same high speed pins that HDMI does in a method that allows for symmetry.