I am not sure I can even find a historical exmample that is even some similar to this situation

Where would you put the Cold War in your schema? Wouldn't you describe that as a culture victory? Certainly today's Russian Federation is showing much the same vigor and malice as the US during our first Robber Baron period. Even Cuba is busily courting tourism investment dollars from everyone with sense enough not to embargo them and there is little doubt they will invite more capitalist interests to the island after Castro finally dies.

As for what-ifs, so-called Communist China is busily using its authoritarian culture (and Wal-Mart's distribution system) to buy the "mortgages" the US federal gov't is steadily accruing against our future success. If in a near decade we see full PRC hegemony on the Asian side of the Pacific Rim and nary a serious shot's been fired, wouldn't that be a cultural victory? It seems a real possibility given Japan's continued state of wealth-constipation and South Korea's need to keep worrying about that funny-haircut guy to their north.

If I was better read, I could probably go on an even better tear about the Catholic takeover of pagan Europe. Sure, arms were involved in far too many a conversion, but dueling world views were definitely very important for the whole process.

The thing is that planets are not contries. Even if you have imperial governement, it is very difficult to control a planet. Take as an example US. If a state decides to declare its independance it can. It will not be instant, but it will take time. An actual possibility is the french speaking province of Quebec in Canada. It tried to declare independace without success for mroe then 1 decade. If they succeed they could then form an alliance with another country such as france or US. The reason would be purely cultural. There would be no military movement or what so ever, since it would go pretty much against constitution.

I dont see why some planets, whose citizens live a cultural life of another federation, could not join another the federation. Obviously it should be harder under the imperial governement and if the troops are present, but it is not impossible.

Finally dont forget the main purpose of the game is balance and fun. The cultural victory is pretty much your choice. I have played the game on masochistic pretty much and the AI never built any decent inluence starbases. Thus if you dont like cultural victory just dont use it.