To start with, I want to avoid the logical fallacy called "exclusion of the middle" which is very common here. Even if you disliked the combat in earlier Civ game there would have been other solutions than an arbitrary 1 unit per hex limit. And for this game and scale I'd contend it is an extremely poor match, and the problems with it make it hard to enjoy the other innovations in the game. To wit:
1) It makes the mechanics of moving clunky and the game run very slow. The CPU is spending all of it's time doing complex pathing calculations to shuffle units around, and the more units (higher difficulty) they have, the longer it takes. Tasks which were never a problem in earlier games (assigning workers to build a road) are tedious and glitchy. Moving large armies is a buggy pain, and units in battle are frequently sent to their death (both human and AI) because it can't figure out how to get from A to B.
2) Roads are not only rare by design (fine) but almost useless in practice because of the stacking limit. Single NPC units can perma-block roads in neutral territory, and frequently do.
3) It distorts the rest of the game. Civ was designed around a different paradigm, and the changes needed to avoid unit overpopulation made the peaceful game imbalanced and boring (e.g. weak production and high costs for large empires, both driven largely by the need to avoid massive unit production.)
4) It is inappropriate for the scale of the game. If you wanted to have fights resolved on a tactical map with no stacking: great idea! But when the British Isles are 4 hexes, for example, it does violence to the feel of the game. And it scales poorly with size: the feel is best when you have a lot of room to maneuver, but the game design harshly penalizes large empires and maps, favoring smaller ones where the stacking limit performs the worst.
4) It's prone to artificial tactics. Once these are widely known the claim that combat is now more "strategic" will be falsified - because it's false. There is a reason why wargames abandoned the "I move and attack, then you move and attack" mode. It's because it rewarded unrealistic tactics, like soldiers darting from building to building and never getting attacked when they cross the street. Modern wargames have things like opportunity fire (e.g. when you move in range of my city, or artillery, then I attack you *first* as you charge at me.) Civ 5 has taken the worst aspects of the alternating turn approach and amplified them - for example, with cavalry which not only attacks first but which can retreat, or with insta-heal combat promotions. To eliminate the extreme distortion of "all my units attack, then you go" it's important instead to give both sides a chance - in other words, if you can damage someone else then you can be damaged yourself when the other guy gets a move. It's basic wargame design, and it was ignored. Civ 5 fails as a compelling wargame because it didn't pay any attention to decades of lessons from the tabletop world (I'd bet the Civ 5 team is utterly unaware of the principles behind the boardgaming renaissance led by German designers like Reiner Knizia, for example.)
5) The new problems created with 1 unit are worse than the big stack problem they solved. No stacking favors big units over little ones, replacing "stack of doom" with "unit of doom". Large armies create gridlock, and the absurd consequence that you can't even use most of your units because you can't even reach the field (in a battle on the size of a continent). This is especially a problem for the AI, which gets clogged and paralyzed with gigantic numbers of units at the highest levels.
6) The above problems cripple the AI as an opponent. It isn't that they didn't try, it's that the problem they're giving the AI isn't soluble. A bigger army can actually be worse than a smaller one because it can't move: that's very hard to program.
Solutions? A modest stacking limit, either with overstacking allowed (but only the "limit" worth of forces permitted to engage in military action) or the AI coded to keep itself 1 or more below the limit at all times (to allow movement.) Unlimited stacking for civilians. Combining units to create armies (and attaching generals) would be a cool idea that would work well. Ranged units can still attack more safely (but don't need to be able to do so from 2-3 hexes), and weak units can be guarded by strong ones in the same hex (a godsend for the AI.) There are plenty of answers to the Civ 4 problem, and unfortunately the Civ 5 model isn't the right one.
