It is a good idea and it needs to be present in the game, but it needs a lot of work in order not to break the game
Culture change must be a slow, costly and risky process because the people will not tolerate this change. And at the same time, we must have the decision in case we decide to change the culture or leave it Also, there must be a way to reduce the risk of change, such as ending missions in the city and eliminating looters, and also using forces such as city culture to be in garrison or marriage.
We must also obtain benefits from this transfer, for example the possibility of recruiting soldiers from the culture of the ruler, and if it is possible to change the design of the city if a certain percentage of the culture is reached.