Why are doomstacks a problem? You can turn off battle animations if it's taking too much time to play them. On the mechanical side in civ4 they are soft-countered by collateral damage.
There's no tactics or finesse with a doomstack. War begins, you dump your stack into the enemy territory, and it boils down to who has a bigger one. There won't ever be any clever outmaneuvering, cavalry will be of limited use, and terrain doesn't matter as much as it should.
All the counter mechanics, like bombardment, collateral damage, changing target priority, nukes always felt ham-fisted to me. Probably the best thing about it is that it's very easy to teach the AI how to work with this: declare war, park your doomstacks on the other side of the border,
move towards a target. Of course, 1 unit per turn brought its iwb share of problems. For all its flaws, GenderNonspecificPersonkind(tm) actually proposes an interesting middle ground here by stacking units into groups of 4-8, then having the battle play out on a designated field. It's far from perfect, but allows stacks to cooperate through reinforcements, and deployment of larger stacks an be limited by landscape, line of sight can be a factor, and battles can be fought over more than one turn. The AI is still rather dumb, but seems to handle itself better than with 1UPT.
When it comes to the dumbing down of Civ, I think the biggest missed opportunity (not necessarily dumbing down) can be seen when you compare it to Alpha Centauri. There was some overlap with a few decent ideas getting into Civ3, but the biggest loss is in the terraformable map and unit editor. IIRC there was some work to mod it into Civ4, but the biggest problem was always in teaching the AI how to work it.
Other than this, it's hard for me to trace a definite trajectory for decline/incline in civ games. The first was of course the most primitive, but each civ afterwards has something that I look back at rather fondly (the built-in copy protection in Civ 1, the tax distribution sliders limited by government, the throne room and the palace from civ 3, etc.) and something I was less than enthusiastic about. What I liked about Civ 4 was it tried to break off from the "carpet everything with cities of your color" gameplay and combat actually started to make some kind of sense (never forget, phalanx killing bombers in Civ1, or a lone spearman killing off a horde of barbarian horsemen by healing himself through veterancy, as seen in civ 3). For this reason, I had some hope for the hexes and 1upt in Civ5, but I never managed to love that game.