I do like the idea of each province having a seperate 'name' so to speak, a provincial name.
Another thing: Provinces are something I would want to begin early in the game, and happen often. I also don't want them to be something too easily decided upon. Therefor, a price closer to something like a Colloseum may be appropriete, or even slightly lower. Provincial capitals need to be an investment, but one that could make creating provinces in far away territories possible.
Yes... provincial cities that are not connected culturally should have some sort of penalty, but I also want to see provinces made up of several nearby small islands, even if they aren't connected culturally yet.
I'll state it again: My idea for province sizes is between 3-6 cities. Not too big on small maps(3), and can get to a decent size for larger maps. (6).
About cities changing provinces: I would imagine a city could join a province after it's formation, and during certain times change province. However, when I think about it, maybe not. Of course, you could always destroy the provincial capital, ending the province entirely to restructure... but what a headache that would be! Also, when you conquer enemy cities, if they are part of a province, and you conquer the entire province, the provincial capital is not destroyed, and you simply own that province as well now.
When it comes to a province's functions, I DO want many interesting effects. However, I also don't want you the player, or me for that matter, to deal with a thousand new things! What I want from it is decreased corruption, a tab on the units created in each province so that if civil war breaks out, those units will follow suit, as well as a province's telling you the things that particular province needs, which would be things they would need anyway, and would mean you can just see what they say instead of looking at the cities themselves (in fact, that could decrease that element of micromanagement at least a little bit!) Provinces would keep tabs on the culture of the province. That means that each city's culture would go together into a provincial culture moniter. You could look at that to see each region's culture, to get a larger picture than just every city. Provinces should be able to pool production, to at least some degree, as well. I also want resource management to have bonuses for provinces. If one province has a resource, and the others don't, when it trades [automatically] with the other provinces, it gains a bonus commerce or two for every other province that takes its resource, without the other losing anything. If you have multiple provinces with that resource, they will be spread along to the other provinces based on who's closer to whom. Of course, if their resource is traded to other countries, they gain more bonus commerce than if they were trading with other provinces. Would be a little bit more interesting resource useage.
Anyway, I know I have more, but I hope I'm getting the point across with this. What I'm trying to convey is that most of these should not increase micromanagement, since they are either automatic, or allow you a broader view on your empire than simply each individual city's needs, definitely a good thing. They should add some more depth, but not a lot more micromanagement. No more so than adding tradeable resources and culture added more micromanagement.
Anyway, I do hope this helps... of course, I'm simply repeating myself, but sometimes the same things get said in this thread... I'll get to more of them later.