...At least that was the intention in ST2.
But the ST2 system was a minor revamp of the TMP system where red collar indicated Engineering (there being no special color for trainees or cadets), and OTOH we have seen Cadet Picard wear the black collar while in the jumpsuit in that ST:NEM photograph.
There have been blackcollared jumpsuit wearers on the bridges of basically every TOS movie era bridge: the E-nil, the E-A, the E-B, the E-C (although admittedly in the aftermath of combat losses), the Excelsior, and the Grissom. All those bridges had a great number of workstations scattered about, many with "standing room only"; this in contrast with the TOS bridge with the limited number of chairs all occupied by the main officer heroes save perhaps for the one next to Scotty's station. Then again, the jumpsuit people in the movies sometimes sat at "main" consoles, like the helm of the Grissom.
There were folks on Captain Pike's bridge who probably were enlisted, too - the character dubbed "CPO Garrison" in the end credits was sitting there, with unique "broken" sleeve braid, and a number of people in uniforms that had no sleeve braid were standing around.
One might speculate that different starships have differently distributed command systems. In some, the actual bridge is designed only for the top officers, and there are supporting rooms nearby with lower-ranking people. In others, those support functions are handled from the main bridge, or at least have secodary stations at the main bridge - and people might rush to those secondary stations if the adjoining rooms were damaged, or in a training situation or on a skeleton-crewed ship where there would be no officer supervisors available for those separate rooms.
Certainly one would see a role for specialized, narrowly trained NCOs and enlisteds on a starship bridge that is full of complex high technology an officer shouldn't be required to master, but that also is often left rather unautomated, or at least with manual overrides for every key function. For example Uhura in TOS should probably have been an enlisted specialist, given her very narrow field of expertise; and perhaps Sulu and Chekov, too. (But it was admittedly quite practical that Kirk could place basically anybody from the bridge in temporary command...)
Timo Saloniemi