Something obvious that I don't think's been said yet is that the capital is very often the largest city, especially in the pre-modern era. This makes a ton of sense, both having the government located where most people are, and with the capital naturally becoming the largest city because of the opportunities that it creates. In any case, I wonder if capitals could give some kind of bonus that scales with population? Alternatively turn it into a malus, where a large population city in the core that isn't capital might create unhappiness/instability. I don't think this should apply to cities outside the core though, and I do think it should phase itself out in the modern era (as no one's seriously suggesting moving America's capital to New York, I don't think).