We already have evidence of at least two eras where the "parade" or "Class A" uniform style is accompanied by coveralls: the TNG/DS9/VOY era and the TOS movie era. We might consider the TOS wraparound coveralls as a third such case; we'll see if the rebooted movies introduce a similar parallel style for the alternate 2250s or early 2260s.
Neither the "A" nor the "B" style seemed to represent fleetwide standard in those eras - but it did take some time for the "B" style to appear in front of the cameras in the TNG era. I'm sort of hoping somebody will come up with a good-looking "A" style for the ST:FC design, too, and retroactively make it look as if "B" never really was a fleetwide standard in DS9, merely something worn by the working stiffs and those more interested in winning the war than in looking good.
For all we know, Picard no longer commanded the Federation Flagship in ST:FC, ST:INS and ST:NEM, and for that reason no longer insisted on everybody wearing the "A" style for the era. It's a bit contrary to that idea, though, that our heroes would be in their best dress uniforms at the beginning of ST:INS, yet the band playing in the background would be wearing humble coveralls...