The real problem that stems from this Cultural Overbuild, imo, is the fact that all of the spaces occupied by those culture centers are spaces that are not (or are no longer) being used for research, production, or economics.
In all of my games, I have found that sometime around the middle of the game, the AI races begin to go progressively passive, dropping farther and farther behind in research and the other categories. (Yes, this is before I start to exterm... I mean, liberate them all.)
I think these culture centers are the reason - the AI factions build so damn many of these things that they can no longer compete in the other areas. And this is in games where I do everything in my power to keep my influence low (no influence mining, no influence starbases, no embassies).
Once the Cultural Overbuild starts, it's like the AI factions have given up. Half the time, they just let their gigantic stacks of single ships sit around in one spot while I zip around and mop up their planets. They are no longer capable of researching new weapons or producing starships because all of their tiles are occupied by these stupid influence structures. It's frustrating to get that far, only to meet less and less resistance as time goes on.
I would like to see culture buildings changed so that only one can be built per planet, and have it generate influence based on the planet's Influence and Morale ratings. Embassies could add the two and multiply by their rating, culture centers could multiply all three ratings. Or something.
I know the AI feels the need to compensate for influence factors, but this slowly kills its ability to compete in all other areas. With some planets, the assault is like taking a Greek ruin - half the tiles are culture centers, the other half are empty. If the AI would just respond more forcefully to cultural threats (like I do), it wouldn't need to cripple itself to stay in the game.