One of the reasons we didn't see many NCOs in trek was Gene thought that in order to be an astronaut they would have to be highly trained, since it was the 60s and space exploration was still a new thing, think about it, most astronauts at that time were Navy and Airforce officers above the rank of Cmdr./Lt. Col. We saw some in the movies, but mainly because of Directors like Myer who wanted a more military feel. Again the first few seasons of TNG were helmed by Gene, hence no NCOs. If I had to make up an in universe reason, it would probably be that maybe it's comparitively easier to get into Starfleet Academy than it is to get into modern military academies, we see children on TNG and DS9 studying Calculus and quantum physics and stuff, maybe there's just a higher percentage of children who meet the requirements to attend.
Personally I use NCOs all the time in my fanfic.
(As any good Chief would tell you, NCOs and Crewman are not the same BTW. NCO specifically refers to Petty officers or Sergeants, not Privates/Airman/Seaman/Crewman, who are Enlisted men.)