I believe that the current system for moving holy cities is lacking in realism.

The non-realistic part is that it moves during Hellenistic times and on. An excellent example of this would be of Jerusalem. As the Jewish holy city, it has been so for about 2000 years, during which no Jewish nations have held the city. A similar one, also attaching itself to Jerusalem, is Christianity. It has been a Christian holy city for a long time, again during which no Christian nation has held it for any significant time.

I am not familiar with cIV coding, so I can only make recommendations. One could be a limit to how many movements a holy city can take. Another being a tech that stops movement from and to a nation. Finally, a combination with that one and a different idea, making a civic, with some earlier tech, that only disallows movement of holy cities and a later tech that disallows them to move without a civic.

I welcome any comments, including any more ways in which to fix, which I believe to be, this unrealistic part.

Its not much realism i agree, but its a bit for ballance. You no longer found every possible religion and get money from all shrines.