Jonathan said:
I've already proposed a solution: battles should be resolved as whole battles, not as a series of single combats. When you attack a square, the game should take into account all the attacking units and all the defending units, resolve the battle according to some formula, and give you an outcome. This is the way wargames have been played for a long time, and it's a better way.
Why better? Because it's quicker, it's easier, and it's more realistic.
Jonathan,
no it's not! For turnbased games where one player follows the other it is vital for strategic decision that you control every single unit. Only that way you can decide "how" the battle is finished. If you have the initiative (it's your turn) you can choose how you attack, if not (it's another one's turn) you can only counter with the strongest available unit.
An example (city promotions): The enemy has 2 archers, one unpromoted as defenders and you 3 swordsmen, one unpromoted. You know that your promoted swordsmen are too weak to kill the promoted archer, so you take the unpromoted first for a lucky hit to do some damage or even but more unlikely get a new promoted unit

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If both enemy archers are unpromoted, you may, of course, take your elite swordsmen because the odds are for you and you do not want to loose your unpromoted swordsman if you can do it without losses.
The warfare in Civ is about deciding what units you take with you and how you use them. That you took the swordsmans sacrifice in the first example is a decision that is risky but it is a decision to be made. If you would decide to take the elite swordsman, it is much more likely to be your loss. But how can a formular decide this?
Putting them all into a stack-vs-stack formular would eliminate this decision. Therefore combined arms, different unit types and promotions would just be a flavour. As you could not decide how you use them they would be just numbers in a formular. In consequence you would not need all this but just could count your overall strength.
Viola! You have eliminated the warfare game element completely.
Ask yourself: What is a game about? A game and game fun is always about deciding. Should I move the king or the queen? What can I expect in doing one or the other thing? When I succeed, I succeeded because of the decisions I made and that's hell a lot of fun

With your suggestion all fun would be about "how much soldiers do I take with me?". A single poor decision that you will mostly answer with "all that I can spare concerning the other battlefields". This is a completely different concept and has nothing to do with a detailed warfare game concept that is fitting to a detailed managing-a-city concept. That is what is this game about: Cities and units. Two equal abstraction levels.
What you want to play is "Risk", I am sure. It is turnbased, you have numbers and you just dice everything out. I want to continue to play Civilization because I want to decide more than just "where do I send my armies and how do I split my force on them?". Risk I do only play on a board with my friends, but on a computer it is boring even or because it is a lot easier and quicker, as the computer dices everything out
Additionally it would be not more realistic at all, of course not! Never in history were battles fought by formulars. A formular can not consider the number of decisions made by a good general (a player) compared to a bad general that may even have a good day (another player). When do I send the cavalry? Where do I put my defenders? How do I disturb the enemies advance?
With units you have this power to decide what to do. You can choose the battlefield if you are a good general. You can decide how you attack and surprise your opponent. And wether you retreat after some losses or not, you may as well decide.
A formular can not provide such decisions that decide about life and death. A general, that is more realistic, can. You are the general. And therefore you want to control what your units do and let it be done not by some formular.
If you want to stick to quick and easy: Feel free to switch on "stack attack" in the game options dialog. It should eliminate your need for a quicker and easier solution to battle other players. But not always the best...
Yours,
Publius