Holy City represents the birthplace of the religion. That's the only logic, period.
Not necessarily. A holy city isn't just the birthplace of a religion. At it's basis, it is a city held sacred or important by followers of a religion. From wikipedia:
Holy city is a term applied to many cities, all of them central to the history or faith of specific religions. Such cities may also contain at least one headquarters complex (often containing a religious edifice, seminary, shrine, residence of the leading cleric of the religion and/or chambers of the religious leadership's offices) which constitutes a major destination of human traffic, or pilgrimage to the city, especially for major ceremonies and observances. A holy city is a symbolic city, representing attributes beyond its natural characteristics.
Also, most religions have more than one holy city, and not all religions have a central authority as the Catholic Church does. Some examples of holy cities:
Catholicism: Rome, Jerusalem, several other cities throughout Europe.
Orthodoxy: Constantinople, Antioch, Jerusalem, Alexandria, and several other cities.
Islam: Mecca, Medinah, Jerusalem, other cities throughout the middle east.
And that's just covering the monotheistic religions of Europe and the Middle East. For Hinduism, Varanasi is only one of seven sacred cities, and I have no idea if Buddhism has a set holy city, but they are very widespread and most likely have several just as the others do.
The place of Resurrection of Jesus becomes the Holy City for Christianity, which is Orthodox as opposed to heterodox teachings of the time (canonical gospels vs apocrypha). Catholicism and Protestantism are developments within that Orthodox Christianity, they were not born from Arianism, for example. Those developments have their birthplaces too. If your Orthodox Christian civilization builds AP in her city -- she claims that the bishop of that city is the only leader of all the Christians in the world. That city becomes a holy city for this new type of Christianity. Which still claims the original Shrine (Church of the Holy Sepulcher, not Nativity) as it's target (crusades).
Not all branches of Christianity work as simply as the Catholic Church does either. Take Protestantism for example. Martin Luther simply voiced his opinion about what the Catholic Church was doing and several different groups sprang up. Martin Luther didn't become the leading ideological figure, nor did Wittenberg (where he put his 95 Theses) become the center of Protestant Christianity. I know there's been debates on this forum before that Protestantism has no real holy city since it's so decentralized.
However, going off the idea that a holy city can contain a religious headquarters, so to speak, it makes more sense that those cities be represented as the major pilgrimage and political centers rather than just keeping it at Jerusalem. Rome is a good example because not only is it the headquarters of the Catholic Church (ok, Vatican City, still inside Rome), it is a huge pilgrimage site due to many holy buildings & shrines and the fact that the Pope is there.
Jerusalem is still holy for Christians today, but it is not as major as it was during the Crusades, especially with the West becoming more and more secular. There are shrines in and near Jerusalem such as the Holy Sepulcher and the Church of the Nativity, but i'd wager that the Temple Mount for Judaism and the Dome of the Rock for Islam attract far more attention, especially given the conflict between those two religions over one site.
Comparisons with the other mods are completely irrelevant here.
I think they are relevant if all the mods are following the exact same model. SOI probably follows closest to the idea of a "religious birthplace" for a holy city, but they still keep the Orthodox Holy City in Constantinople. and RFC Europe doesn't have space for Mecca, so the Islamic holy city is in Damascus, which was the capital of the Umayyad Caliphate when it first started.
EDIT: Plus, if we keep the two Christian holy cities in Jerusalem, we'll only make Arabia more of a monster with the extra shrine income. I don't think most of us would like to see that since there are so many complaints of Arabia surviving well past the arrival of the Ottomans.
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Most people here would not appreciate the 
