I agree that the officer/enlisted divide should be much different than we tend to picture today. The division is based on the idea that people born in a certain social class are leaders, the others are followers, and the two shouldn't mix. In the 20th century, education basically took the place of social class, especially in the US, but that's how the division originated.
A hundred years ago, the vast bulk of armed forces were unskilled or semi-skilled labor, and it was common for a private first class or able seamen to have twenty years service. Today, of course, it's vastly different. Associate degrees are very common, with many colleges giving credit for military school training, and it is increasingly common for E-7 and above to have bachelor and even post-grad degrees. The education requirements will only go up as technology advances. What will "enlisted personnel" be like after another couple hundred years? Well, who knows, but my guess is the division will be much more blurry.
Certainly, the complexity and cost of space travel, initially, will require small crews of highly skilled individuals. In that sense, the service would probably evolve more like an air force than a navy, with fewer high skilled positions for "flight" operations, more but still highly skilled "ground" jobs, and a few less-skilled still in training. And as the technology advances, qualification level goes up, numbers go down. I've used the example of the early USAF: A B-29 had a crew of four officers and seven enlisted, ten years later a much more powerful B-52 had five officers and one enlisted. And as the youngest US service, the USAF has the most "casual" officer-enlisted relationships and their enlisted personnel live less-regimented lives than those in the older services.
Another factor is physical separation. On a battleship, cruiser or carrier there was enough space for the officers, warrant officers, chief petty officers etc. to keep to their own turf. On a destroyer or a submarine, not so easy. Familiarity breaks down social barriers. In a small-crewed spaceship, a person's rank wouldn't be as important as his/her job and performance.
As space ships get into the hundreds of crew members, one can imagine a lot of the former "ground" jobs being absorbed into "flight." Also, in a ship with a scientific mission, many of the additional crew will probably be there for scientific/academic qualifications, the descendants of NASA mission specialists. But I think by that time, much of the old social separation would have broken down. There would be more of a continuum of highly skilled "non-commissioned/petty officers" and and highly skilled but more managerial and leadership-oriented "commissioned officers." Moving from "non-com" to "commissioned" would be common, based on performance and ability. I put those terms in quotes because those distinctions may well be abandoned by that time.
And that's not even addressing the implications of the ideas of the Federation as an egalitarian Utopian society, or of Starfleet being non- ... well, I won't say it.
I also agree that the enlisted portion of Starfleet was not really given much thought in any of the series. From what we see, though, the visible and social distinctions are minor (except for the retrograde WOK enlisted uniforms, which were a money-saving way to use jumpsuits left over from TMP).