Good points. But they don't explain this arbitrary dichotomy.

it could have three or more groups instead of two,

Indeed it does -- 23 or so groups, which are the ranks.

I suspect that cutting off lower-ranking officers from fraternizing with enlisted men prevents what would otherwise be one of the more common problematic cases.

That's plausible, though we should be cautious of reverse reasoning: Did the Lieutenant/Sergeant border arise to prevent fraternizing across those levels, or is fraternizing across those levels considered extra-bad becauses it crosses the officer/NCO border?

I am not convinced that this is a good explanation for why the dichotomy exists in the first place.