I get that you like that. But I don't think it is realistic. It makes sense that losing a super high level unit would be a serious blow. Taking casualties should be costly. And it is good strategy too. There needs to be a cost-benefit to player's actions. Yes, you can play more aggressively but it is a bigger gamble. It might pay off big or lose big. That makes your decisions more interesting.
This unit differentiation between amateur (green, militia, etc) and professional (veteran, elite) is at the heart of all good miniatures wargame rules written and published in the last 50 years, so the miniatures people have spent a lot of time on it. Since I were one of those up until my arthritis made painting miniatures no longer possible, and helped write several sets of rules, here's my synopsis of what worked.
Better troops not only inflict more casualties, they also suffer fewer casualties - as one of the rules writers put it neatly, "The first thing you learn is how to duck." That means the 'elite' unit you have spent much time and resources promoting will be harder to destroy all other things being equal. And while you are trying to destroy it, it will be chewing up your 'mass' units at a fearsome rate.
Another criteria: even when an elite unit is destroyed in combat against overwhelming numbers or forces, its story doesn't end there. Frequently it creats a Legend that lasts for centuries. Think of the 300 Spartan Knights at the Hot Gates (Thermopolaye), the 65 French Foreign Legionaires at Camerone, Mexico. The US 7th Cavalry Regiment still celebrates Greasy Grass (Little Big Horn), despite the fact that it was militarily and tactically a disaster.
These Legends are extremely powerful: I doubt that most of us would know anything about classical Sparta were it not for the sacrifice at Thermopolaye, and I doubt that 1 in 50 of us even here in a relatively-knowedgeable Forum group could name any of the battles that the Spartans won to make their reputation as elite troops before Thermopolaye. The Battle at Camerone quite simply made the Foreign Legion: as it is still said about it: "This is what it means to be a Legionaire".
As to the mechanics, a game at Civ's scale does not need the detail that a tactical game needs. I suggest, in fact, that Unit distinctions could be reduced to Amateur and Professional.
Amateur would be the bulk of drafted or conscripted troops, raised as needed, not costing much to maintain because they cannot use sophisticated weapons, but also taking heavy casualties because, as posted, they don't know how to duck. This kind of force dates back to the earliest urbanization: Sumer, Egypt, Chinese Dynasties at the earliest all relied on spearmen or slingers/bowmen called up as needed, occasionally given land to support themselves when not called up to fight, and given little in the way of training or permanence.
This would result in a whole new (for Civ) Unit Mechanic: the number and type of units available to be raised for the duration of the war would only appear, normally, at the start of the war and would be based on the productivity of the Civ: how many tiles of farms, mines, foresters or camps, how many production buildings, - even Wonders of certain types. The type of unit available could even be dependent on what they do as civilians - your number of slingers/archers could be dependent on the number of camps or farms where people have to hunt down predators or destructive wildlife with slings or bows every day. Other types could be dependent on Social/Cultural aspects. The Greek Hoplite, an amateur except in Sparta, was called up from a middle class that could afford the expensive Hoplite array of heavy wood, leather and metal shield and leather and metal armor. Your social standing depended on both your ability to afford that array, and also your willingness to keep yourself trained to use it in the
Gymnasium.
Professionals are the troops that stick around after the fighting: the Chief's
comitatus or personal guard of warriors, or men with weapons that require constant practice and training to use well, like swords or mounted lances. These units are expensive to maintain, because they must be maintained constantly: fed, housed, kept on hand to train and practice even when there is no war or fighting going on. The Imperial Roman Army was all Professionals - over 50 Legions plus Auxiliary units - and that army, in the end, bankrupted the Empire that had lost too many productive, tax-paying civilians to plague to afford it.
There could be a third distinction: Heroic or Elite units. These are the troops who create the legends mentioned above. The 300 Spartan Knights (a latter-day version of the old Indo-European chief's
comitatus) or the best of the European states' much later Guards units, whose performance was summed up in the reply at Waterloo: "The Old Guard dies, but it does not surrender." (The Old Guard
Grenadiers a'Pied, in fact, is the model for Civ VI and VII's Garde Imperiale Unique unit). These would be very expensive to obtain and keep, but also very hard to kill and potentially create a Legend that transcends the Ages for your Civ or Civs - we are, after all, still celebrating the Spartans 2400 years later.