I've never really gone back to ENT beyond the first time through, so I don't remember much of the details about that show. I do seem to recall that at one point they had a detachment of marines on board. That, combined with the relative youth of Starfleet and Earth's space exploration would easily explain the difference between their crew and the crew of a ship like Picard's Enterprise.
DS9 was more of a frontier, roll up your sleeves (literally, for their first uniforms) and get to work sort of show, so it makes sense there as well.
But it's funny you mention TOS, since I looked up a list of enlisted characters and it was weighted pretty heavily towards that show and the movies. Half of them seemed to be either attractive yeomen that we could ogle through that silly filter they put over close-ups of women in TOS, or miscellaneous names from The Wrath of Khan and The Undiscovered Country that are only known because they were tagged that way during an auction of the props.