It looks for me that CMFB is to control the circuit under small condition only
As you probably know, a differential output stage absolutely needs a CMFB, because otherwise the output levels would be undefined.
So CMFB's mission is to keep the voltage levels of the differential output stage in the mid-range of the operating voltage, in order to allow for max.
Output Common Mode Range (OCMR), irrespective of the inputs' position anywhere in their ICMR.
Now under large signal / fast step conditions, I think it is particularly important to keep the outputs' levels in an optimal position for largest possible OCMR - and this fast enough for such fast slewing conditions, because the full output range is needed for both outputs. IMHO the CMFB circuit must react
even faster than the output stage, in order to fulfill its task well & fast enough, which means
even higher pole(s) resp. fT frequency than the actual diff amp. You know what this means for the CMFB's operating current.
I remember I've read a paper about this context, but unfortunately can't find it any more.