Military officer here. This is actually quite a bit more complex of a question than I expected going into here. Much of what US military officers learn about their own history must be taken into context: the US experience (and reasoning) for its structure has shaped American reasonings for the divide between enlisted/officers up until the 20th century that was often different from European nations and other nations around the world.

It was in the 20th century, however, that the two-tier system became codified across militaries around the world by the laws of war.

First of all, a lot of what is mentioned about historical precedence with nobility - and going far back to the Romans, the relationship between nobility and the centurion and his legionnaires - is often cited, and there are certainly military traditions that harken back to those days (such as the origin of the salute being from the times when you would raise the visor on your helmet so a superior can see your face), but many of those relationships are explained more as tradition than anything else.

There isn't a clear delineation of when certain aspects started. Indeed, keeping in mind that many nations take their military customs and traditions from predecessors, it's often been a gradual evolution over time.

For instance, with armies, we've seen throughout feudal society the clear delineation between nobility and the peasantry. As thus, many feudal armies consisted of nobility leading those levied from nearby lands (the enlisted). An outcome of this has been that to address a superior, especially an officer, you say "sir/ma'am"

It's important to note too that the different branches of the military have different histories regarding this. In the Navy, for instance, naval ranks have had different origins than army ranks. For instance, Ensign (O-1) - quite literally flag-bearer -was written in Thomas Venn's Military and maritine [sic] discipline (1672) to mean the bearer of the flag/colors and assistant to the captain and lieutenant.

Of course, the clear line between officers and enlisted on ships comes from the fact that officers are commissioned by the sovereign of a nation - and given certain authorities to carry out actions/orders on behalf of said sovereign. Indeed, to command a warship - commissioned by/on behalf of said sovereign (e.g. His/Her Majesty's Ship (HMS), United State's Ship (USS))- it required said commissioned rank. And to delegate said authority to subordinates in his stead, any captain of said ship had to have commissioned officers.

With navies having been historically professional militaries, under the authority of the sovereign/central nation, before armies became professional standing armies (e.g. the Royal Navy being nicknamed the Senior Service), that tradition has been in place in nation's armed forces for quite some time.

See: The navy.mil history page explaining origins/roles of some maritime ranks and their duties

That touched upon the part that I wanted to get to, which is why a commissioned officer exists. Take a look at the oath of enlistment versus the oath of office for commissioned officers, from the history.army.mil website:

I, _____, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God." (Title 10, US Code; Act of 5 May 1960 replacing the wording first adopted in 1789, with amendment effective 5 October 1962).

Versus:

I, _____, having been appointed an officer in the Army of the United States, as indicated above in the grade of _____ do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic, that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservations or purpose of evasion; and that I will well and faithfully discharge the duties of the office upon which I am about to enter; So help me God." (DA Form 71, 1 August 1959, for officers.)

If you're interested, this piece hosted by the Air Force about the Oath of Office, goes into more detail about the intricacies and history of hte wording of said oaths.

To be a commissioned officer in the military - and this is something Article 2 of the US Constitution explicitly states - one must be appointed by the President (or on behalf of the President). As thus, one "assumes office" on behalf of the nation.

Historically, one can look too at the naval expedition by Commodore Matthew Perry to Japan - he was able to directly conduct diplomacy with the sovereign head of state of another nation on behalf of President, the chief diplomat of the nation, as he was commissioned into office and assumed the duties to do so.

Likewise, with the US President being Commander in Chief, said duties of command are officially delegated downwards only to commissioned officers, who are thus the only ones legally capable of commanding ships, aircraft (all pilots in the military are commissioned or warrant officers), or other organizational units (e.g. platoons, companies and battalions on up).

As for why all of this merged in the 20th century - this pdf from the US Marine Corps' Laws of War course touches a bit on this. It mentions the Hague Convention of 1907 and Geneva Convention of 1949 where a lot of rules regarding the conduct of war were codified into international law.

Various rules and laws - often drawn from custom and tradition - were codified, and this included the roles and responsibilities of officers (for instance, little known rule but all non-officer prisoners-of-war must salute all officers of the detaining military while in captivity) which has gone on to be adopted worldwide.

Another question on the subject. Is there evidence of extremely/"very" successful military compositions without the two tier of system? Let's say... 1600 onwards?

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I would also be curious to see an informed answer. I've read that Rome had newbie nobles that were advised by Centurions and other veterans, and am familiar with the U.S. practice of throwing new 2nd Lieutenants/ensigns into units to learn from veteran NCOs. Where did this begin?

In many businesses, (at least, in labour intensive industries) there's a clear line between workers with hourly wages, and managers with yearly salaries.

Can you expand on the difference between this system and a 'business management' system?