And why would we want to do that?
I'm not sure what the advantage of getting rid of "non-graduate entrants" entirely, as
on screen canon has always clear that specialist personnel junior to ensigns do exist.
The most obviously
recurring and unambiguous examples examples of this would be Janice Rand and Miles O'Brien.
However, if you focus on the part about an "enlisted and officer divide" and "high school educated enlisted men", then there are a number of workarounds that are consistent with
on screen cannon.
The easiest to explain option is that Starfleet "crewmen" are essentially equivalent to the Age of Sail "midshipmen", which were direct entry recruits working as (senior) deckhands training onboard ship (in the words of Simon Tarses "out there, travelling the stars"), but
training as (commissioned) officers and mates (roughly equivalent to modern petty officers).
This also roughly corresponds to the system used in most police departments, and has some similarities to the Royal Navy commissioning system compared to the American "graduate only" system, although RN officers do get the equivalent of an Associates Degree before making Sublieutenant [O1] (~ USA Specialist [E4] or USAF Airman 1st Class [E3]) and many
do get a Bachelors before their first command.
YMMV, but my preference is always do figure out a way to make things work, particularly when BTS material (secondary canon at best) conflicts with apparent
on screen (primary) canon.