Differential output voltage (e.g. Vo+ increasing and Vo- is decreasing) can't change the CMFB voltage.
But if the output common mode voltage is increasing (Vo+ and Vo- are increasing), than the current through the Mm6 will increase. It will increase the CMFB voltage too, which you can use to control a tail or head current of a differential amplifier.
CMFB sets the transistors into the correct operation region, and single-ended amplifiers don't need this, because the used one negative feedback around the amplifier is enough to set the transistors.
Single-ended amplifiers doesn't have got common mode output.