In regards to the "Well, it requires more thought!" argument for EITHER stacks OR 1UPT, I think it's ultimately a wash.
It's not that one requires MORE though than the other, but rather that the thought process is different. And both are fairly simplistic.
Consider for a minute.
With stacks, you had to decide on the composition of the stack to start with. Were going to make a city-busting stack full of CR units and cats? Did you have enough medic units in the stack to heal your units between turns? Did you have enough garrison troops to leave the city in relatively safe hands, quell revolts, and fend off counter-attacks? How about countermeasures; were you adequately armed against what the enemy had? (IE: mounted units to attack his siege weapons, spears/pikes to defend against his mounted units, etc.) Were you making a pillaging stack? Because that'd require slightly different composition. Once you were in position to attack, how did you handle the attack itself? Launch your cats forward to suicide and wear down his city? Hit it with your weaker troops at the risk of losing decent garrison units? Or hit it with your more advanced troops (IE: CR3 macemen) and risk losing THEM and your ability to push forward? The approach to a given site of battle counted, too. If you're going to besiege a city for several turns, are you crossing a river? On a forested hill? Did you manage your approach well enough to get into position with moves left to fortify? You had to think plenty. It wasn't just "smash your stack into his and see who wins." Plus, your production, technology, and wealth all mattered. You had to manage ALL of that in order to field a successful army.
1UPT also includes some thought, but it's a different kind of thought. You still have unit countering to deal with, but you also have to lay your army out carefully so Unit A doesn't block Unit B's approach. All this is is a different KIND of thought, though. You're dealing with a certain kind of spatial thought, akin to those puzzles with a missing tile when maneuvering. Sometimes you have to decide whether you'll approach one way or another, based on the 1UPT limitations. Obviously, your production, wealth, and research all still matter, but you are often fielding FAR fewer units (due to slower production times), you have to contend with relocating units (which takes FAR longer due to lack of roads often), and you have to think differently about fighting. But I don't think this is MORE complicated than good management of stacks. It's just...different.
I agree that unlimited stacking with no penalties is a problem. EU3 manages this by having your armies suffer from disease, especially as your "stack" gets bigger. I think that's one decent way to make it less attractive to just build Stacks of Doom. But regardless, an unlimited stack with no penalty does have its problems.
What I see as the fundamental flaws with 1UPT, though, are two things:
1.) The rest of the game had to be managed to (ideally) avoid the "carpet of doom" scenario. Meaning that production, tile yields, costs for EVERYTHING had to be made higher. Road spam had to be avoided so you couldn't just move your armies as a spread-out stack right up to your enemy's doorstep and spank him. And so on, and so forth.
2.) The game's maps are not set up to accommodate large armies with the 1UPT restriction in place. (See also, avoiding carpet o' doom) Unlike, say, Steel Panthers/Squad Leader, the scale of Civ's maps has always been a bit fuzzy. None of that mattered, though, when you were dealing with stacks, rather than 1UPT. It doesn't matter if the Italian peninsula is one hex wide. You could still field the Roman legions with ease if you wanted. Not so with Civ 5. While it doesn't happen on every map, you can find yourself in situations where you're SEVERELY limited in your ability to produce and/or maneuver even a reasonable, smaller Civ-5-sized army. Plus, 1UPT really ends up highlighting some of the absurdity of the map scale weirdness. So, you've got a ranged unit that can literally fire from Gibraltar to Morocco? Seriously? Again, this was always present in Civ games, but it was less ridiculous because you could stack. There was less a suggestion that the scale of the landmass you were occupying was so small as to only perming one "unit." The 1UPT approach also calls into question what exactly a "unit" represents. A regiment? A battalion? A full army in and of itself? Four dudes with clubs? Nobody knows. It never mattered before, but with 1UPT, you impose a sense of scale on a game that previously didn't really concern itself with scale at all.
I'm not against tactical wargames at all. I love the hell out of Steel Panthers. It holds a very dear place in my heart. Same with Battleground Waterloo and such. But those games have rigid systems of scale, and are actually EXTREMELY sophisticated, rather than "tactics lite" like you get with 1UPT in Civ. There's no unit morale to consider, no loss of unit control due to being too far from a command unit, no penalties for shooting through or moving through rough terrain, no unit suppression, line of sight only matters a little bit, etc., etc., etc.
Put simply, the only thing that 1UPT did was to (A) take the stacks and spread them over a wider area, and (B) screw with production and civilization growth as a necessary but ham-fisted way to avoid carpets of doom.