We do know that the specific term "Crewman 1st Class" still exists, as it was applied to Simon Tarses in "Drumhead". Tarses wore nothing on his collar or sleeves to differentiate himself from the supposed 2nd or 3rd Class Crewmen.
Possibly the insignia do exist but are for some reason optional? In late DS9, O'Brien wore a collar plate that gave his rank in very specific symbology: three chevrons and two stars. Supposedly, this would be the second Chief Petty Officer rank, with each star denoting a level in the three- or four-level hierarchy of CPOs; each chevron would dictate a level in the Petty Officer hierarchy. Yet in early DS9 and late TNG, all this was hidden from the audience, and all that could be observed was a "generic NCO identifier" in the form of a dark pip. Perhaps in like manner, Crewmen can have collar plates giving the exact Class, or then go generically with a clean collar.