The problem wasn't with the idea - that sort of customisation is indeed one of the best features of a 4x game; it's the principal reason the first two Master of Orion games were both so good and so fondly remembered. The problem is, it's an extremely bad fit for a Civilization game, which lacks a tactical combat system and has a grand total of three stats. For anyone who, like me, came to Alpha Centauri from MOO, it was a particularly disappointing implementation.
The AC system is similar to a system in a recent 4x space game called Endless Space: you unlock modules in the tech tree that add +1 to your weapons, armour, or shields, and the system does the fighting for you. Endless Space is not a very good game, in large part because like most space 4xes (including MOO) - and unlike Alpha Centauri for the most part - it is heavily combat-focused, and its combat and customisation systems are so poor (for some reason, nearly every space 4x - despite keeping ship customisation - has long since lost a tactical combat system, including Master of Orion 3. It's why games like Galactic Civilizations aren't as fondly remembered or, frankly, as good as the game that inspired them. These games seem to miss the point that most of the fun of outfitting your ships with missiles rather than graviton beams, or with black hole generators, was so that you could actually fire those missiles and black hole generators yourself).
But more than that, functionally the AC system was entirely redundant, which is why I describe it as needless micromanagement. Compare with Civ 2 - a Warrior had stats something like 2/1/1, a spear was 1/2/1, a horseman 3/1/3, that sort of thing. Now, Civ 2 could just have implemented a generic 1/1/1 Warrior, and different techs unlocked an axe (+1 strength), a spear (+1 armour) or a horse (+2 movement), but what purpose would it have served? You just force the player to spend time building the same 1/2/1 spearman design every time they start a new game simply in order to have a unit the system as implemented does for you.
The AC customisation seems cool at first, which is why it's a gimmick, but then you realise it simply isn't adding anything to gameplay but makework, and you're always making the same 6/1/3 buggies in every playthrough anyway, and so just unlocking a 6/1/3 buggy unit would be a lot more convenient and would lose no functionality.