In fully differential amplifiers, what you see is a current source feeding the current sink.
It is impossible to have both currents exactly the same, and whoever "wins" will likely push the other one out of saturation.
The CMFB essentially makes one of the them adaptive to the output voltage, such that both operate in saturation.
A single-ended amplifier only has one current source (or sink) calling the shots. The other just mirrors the current, so no contention there.
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Just realized this thread is 4 years old.
Bummers.