Just as a note,
In a sub, the Chief of the Boat (COB) or on a surface vessel the Command Master Chief officer, while being NCOs, are generally the third most powerful/respected members on the Boat or ship. (Right after the Captain/commander and the XO) For example, if the Commander wants to bounce ideas off his command staff, the first person invited will be the XO, then it will be the senior NCO. (If your in the army, it would a rank of Sargent depending on what size unit it is.) While they do not have the academy background, many times they will have more years of experience then the Commissioned officer, and a much stronger idea of the technical issues.
A really good example of this is on the episode where the defiant is stuck in a gas giant fighting sub style with some other ships. Worf is his usual blunt self, and O'brien, who cannot order Worf to do anything, pulls him aside and gives him advise, which Worf listens to. This is a good example of a Senior NCO-Officer relationship.
Though the best example is most likely the TNG episode disaster, where troi of all people is the command officer, she knows she is out of her element, so she does the smart thing, and asks her senior NCO what are valid options, makes a command choice, and it is carried out.
As shown on TV, Starfleet is officer heavy and the officer does a lot of hands on work compared to the current miltary. then again, since Starfleet has a strong science and engineering backgrounds, and many of those would have extensive post secondary educations, perhaps it not a shock that they have a lot of officers.