I talk about the culture generally from my first post, at least I want to.
I think the culture is too useless because there is little longtime benefit. The advantages of high culture you said are listed and I do not think they stand:
1.Culture is still useful in the newly conquered cities to convert the population;
2.You early warning vision against barbarians;
3.Culture can be used to block the spawn of lesser Barbarins.
For 1, culture does not work well. I'm not able to give the reference of how to calculate the culture percentage in a plot especially in a city plot, but I think this won't trouble you. The conclusion is that how many turns the city generate culture is much important than how much culture it generate 1 turn. So convert the populations in a conquered cities in a few turn is impossiable.
For 2, the dominate fact to fight against barbarians is the number of unit instend of culture. Fighting against babarians is a very important part of a stratagy, if someone only remenber to defend babarians after see them, he or she would be defeated all the time. So a earlier warning is no use. For example, when I play a french game, I train at least 6 archers or swordmen and a settler to settle on a hill on the east border, then all the barbarians in the mid-europe come. The city may be attacked 10 times in a turn. If I do not have at least 6 defenders in the city, the attackers have a very fat chance to kill at least one. And once I lost a unit, if I can not move another one to the city, more units would be lost in the next turn and the city would lost in a few turns. In cases like this, culture helps nothing.
For 3, if you train enough units, spawn of babarins is a bonus instead of a penalty. Barbarians provide so much experience for my units that sometimes I hope there are more babarians. Continue the french game, the city defence trains several archers and swordmen with 3 promotions which help me very much in the later game. The swordmen with city raider II or III help me to conqure cities around very much they have very good odds even when versus crossbowmen so the Bergundy and German civil can be destroyed easily 5 turns after they spawn. The archers with 3 promotions help me to defend the north berserkers, I even do not need to build a city wall.
In BTS, culture provides defensive bonus. More important thing is that the bonus is balanced very ingeniously. For example, consider axemen with city raider I vs. archers with no-promotion (a representive early rush). When archers defend in a non-culture city, axemen wins more but if the city has 10 culture, archers wins more. 10 culture may change the result of a war. If whether the city has no culture or 10 culture, the axemen or archers have their advantage, the value of the culture would decrease very much.