In regards for the rank structure, aside from shuffling Colonel and Major since you do seem to be going for real life equivalents and responsibilities, I'd recommend throwing in a Sergeant rank and maybe a Master Sergeant Rank above Soldier/Private to represent NCOs and SNCOs.
My reason for suggesting the two additional ranks is because, IRL, enlisted promotion tracks are completely different from officer tracks and have been for basically as long as they've existed almost, and while it's possible to move from enlisted to officer, it's not like Call of Duty where once you hit the end of the enlisted track, you suddenly become a lieutenant. The reason for this is two-fold, in that enlisted and officer ranks have different responsibilities and, for a great part of history, there was a massive difference in education and expectations. Enlisted outnumber officers by a wide margin, and make up your average enlisted fighting man, as well as logistics, administration, and basically all that other stuff. Officers aren't the only leadership though, as obviously there is a rank structure for enlisted personnel, broken up roughly into Junior Enlisted, Non-Commissioned Officers (NCO), and Staff Non-Commissioned Officers (SNCO). NCOs are just the guys in charge of all the junior enlisted, like a manager. They're people with a bit more experience than the junior enlisted, and in combat take the role of squad leaders and the like, and often take on other smaller managerial roles in addition to their usual NCO duties as well. SNCOs, who are even higher up in the rank, take on an even larger managerial role, and are generally tasked with making sure everyone is up on training, morale and discipline are good, and acting as a sort of advisor to officers in charge for the "enlisted viewpoint" of things. By this point, an SNCO has largely stopped doing "work" relating to his job, such as infantryman, admin, intelligence and the like, and is more around to make sure guidelines and regulations are being followed.
Officers, generally being better educated, were given more immediate leadership positions, and even modern day officers are required to have a college degree of some sort before even entering Officer Candidate School. A single lieutenant is generally given leadership over a platoon, and they're often tasked with more overarching leadership functions than an NCO or SNCO. While enlisted leaders are (or at least should be) more worried about troop welfare, officers are tasked with ensuring whatever mission or task at hand is accomplished, along with a lot more administrative functions that, while they often delegate to enlisted leaders, they are still ultimately responsible for. An example would be if a unit is given a set of expensive gear, let's say some radios in a real life example. It would be an officer who signs off on them and takes ultimate responsibility of them if any are lost or stolen, though he might delegate responsibility of handling this equipment to an NCO or SNCO, who would be the ones maintaining and issuing them out to troops. In terms of combat positions, most officers don't do the whole "leading from the front thing", at least in the modern day with communications equipment available. Historically, any officer had to march with the army, simply due to the fact that in order to pass orders, you kind of had to be there in person, but even then, it's unlikely for them to be extremely far forwards, but once you get fairly high up on the ranks, you really stop being what's called a "field-grade officer" (which is of course someone who leads from the field) and are delegated to planning in tents behind the frontlines, or perhaps even sitting in on meetings back home while the fighting goes on elsewhere. On another note, there are very often multiple officers in a single unit. For example, a company might have a single lieutenant in charge of each platoon, but will often have both officers and enlisted working as a headquarters element for the company, and this goes on all the way up through the battalion to the regiment, and so on.
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TL;DR: Enlisted and officers are two entirely different promotion tracks for, at least historically, very good reasons and this is before getting into warrant officers, which are something that admittedly not every military has. You could do some arguing in the modern day considering how far education has come, but due to how it's developed, the roles have their own functions and purposes, and while I understand this should be simplified for the sake of ease in RP, I feel leaving enlisted with only a single "soldier" rank is a bit too simple for the complexities involved, and so I'd recommend at least throwing in a Sergeant and a Master Sergeant rank in there.
My reason for suggesting the two additional ranks is because, IRL, enlisted promotion tracks are completely different from officer tracks and have been for basically as long as they've existed almost, and while it's possible to move from enlisted to officer, it's not like Call of Duty where once you hit the end of the enlisted track, you suddenly become a lieutenant. The reason for this is two-fold, in that enlisted and officer ranks have different responsibilities and, for a great part of history, there was a massive difference in education and expectations. Enlisted outnumber officers by a wide margin, and make up your average enlisted fighting man, as well as logistics, administration, and basically all that other stuff. Officers aren't the only leadership though, as obviously there is a rank structure for enlisted personnel, broken up roughly into Junior Enlisted, Non-Commissioned Officers (NCO), and Staff Non-Commissioned Officers (SNCO). NCOs are just the guys in charge of all the junior enlisted, like a manager. They're people with a bit more experience than the junior enlisted, and in combat take the role of squad leaders and the like, and often take on other smaller managerial roles in addition to their usual NCO duties as well. SNCOs, who are even higher up in the rank, take on an even larger managerial role, and are generally tasked with making sure everyone is up on training, morale and discipline are good, and acting as a sort of advisor to officers in charge for the "enlisted viewpoint" of things. By this point, an SNCO has largely stopped doing "work" relating to his job, such as infantryman, admin, intelligence and the like, and is more around to make sure guidelines and regulations are being followed.
Officers, generally being better educated, were given more immediate leadership positions, and even modern day officers are required to have a college degree of some sort before even entering Officer Candidate School. A single lieutenant is generally given leadership over a platoon, and they're often tasked with more overarching leadership functions than an NCO or SNCO. While enlisted leaders are (or at least should be) more worried about troop welfare, officers are tasked with ensuring whatever mission or task at hand is accomplished, along with a lot more administrative functions that, while they often delegate to enlisted leaders, they are still ultimately responsible for. An example would be if a unit is given a set of expensive gear, let's say some radios in a real life example. It would be an officer who signs off on them and takes ultimate responsibility of them if any are lost or stolen, though he might delegate responsibility of handling this equipment to an NCO or SNCO, who would be the ones maintaining and issuing them out to troops. In terms of combat positions, most officers don't do the whole "leading from the front thing", at least in the modern day with communications equipment available. Historically, any officer had to march with the army, simply due to the fact that in order to pass orders, you kind of had to be there in person, but even then, it's unlikely for them to be extremely far forwards, but once you get fairly high up on the ranks, you really stop being what's called a "field-grade officer" (which is of course someone who leads from the field) and are delegated to planning in tents behind the frontlines, or perhaps even sitting in on meetings back home while the fighting goes on elsewhere. On another note, there are very often multiple officers in a single unit. For example, a company might have a single lieutenant in charge of each platoon, but will often have both officers and enlisted working as a headquarters element for the company, and this goes on all the way up through the battalion to the regiment, and so on.
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TL;DR: Enlisted and officers are two entirely different promotion tracks for, at least historically, very good reasons and this is before getting into warrant officers, which are something that admittedly not every military has. You could do some arguing in the modern day considering how far education has come, but due to how it's developed, the roles have their own functions and purposes, and while I understand this should be simplified for the sake of ease in RP, I feel leaving enlisted with only a single "soldier" rank is a bit too simple for the complexities involved, and so I'd recommend at least throwing in a Sergeant and a Master Sergeant rank in there.