Still, I think that organizations do change, sometimes keeping historical forms as an archaism.

That's not a "still", it's exactly what I meant. After the original ladders take root, it is much harder to reform the whole system than to adapt it to the changing circumstances.

I can easily imagine a counterfactual historicla shift where sergeants' social status rises and lieutenants' social status falls, to the point that de facto the strong boundary between officers and non-officers disappears.

I would like to see such ladder inversion examples. While it is true that a new lieutenant has to learn from his or hers sergeant before really talking command, there is still a difference in the social status and education between them.