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.
That is a thing in Civ: Cities represent both cities (as major population centers) and also governmental regions (the tiles around the cities are like real-world provinces, with the city itself as the province administration center.). Actually, every single tile that was notable enough in real life to get a represention via a named tile in RFC/DoC, was the seat of a major provincial government center. The "customizable" thing is just that the player chooses one of his cities as the empire's capital; and this capital gets privileged treatment that usually lets it grow larger.
So, it goes the other way round: Cities weren't chosen as capitals because they were largest, but they were largest because they were capitals.
the whole point of the thread is to find incentives that motivate historical as opposed to ahistorical behaviour. Before adding mechanics that incentivise ahistorical behaviour I would rather not add anything at all.
Okay. There has already been the comment that most historical capitals are inside the core. For the AI, that should be made a requirement (as long as a civ has a core city, said core city should be the preferred capital). I can think of five in-game examples where the RL civs intentionally moved their capital outside of the core. And all of them are already modelled perfectly in-game: RL Rome and Portugal moved the capital outside their core, which created an offshoot civilization (Byzantium/Brazil). RL Mongolia and Phoenicia moved the capital outside their core, and the core shifted/expanded. RL Macedonia moved the capital to Babylon, and collapsed into civil war soon thereafter.
Since the AI rarely moves the palace intentionally, I think that your concern is humans playing ahistorically. I can think of two reasons for humans to do that currently: maximize tax income (which is not a historical reason, the whole distance penalty has some historical merit but is mostly a balancing factor against cherry-picking super-empires) and civ-blocking (very cheesy: you can obstruct spawns and block re-spawns by setting up your capital in foreign cores). Both of these reasons don't match real-world reasons. One of the most pervasive motivations is the increased reputation (and orderliness) of a brand-new, planned, megalomanical city. (Like: Beijing, Washington, Future-Egyptian-Capital, Brasilia, Dur-Kurigalzu, Naypidyaw, New Delhi, ...) or at least a re-organized, major-upgrade infrastructure project that whips the current capital up to speed.
These considerations gave me three more ideas for a potential change, but I can't really know how they might harm the gameplay. They're not necessary related and can be implemented individually.
- The seat of government is restricted to the core and historical area: no more foreign capitals. No change to the current mechanic for core area capitals. But historical area capitals increase the basic maintenance costs for the whole empire (penalty!) while also counting as an additional core tile (bonus). That measure is to stop human players from foreign-core-blocking, but is not railroading them with a "you can only build capitals in core". Players would still be able to move the Russian capital to Wladiwostok though.
- A civ starting in late classical or in early medieval age has a "Palace III" in the capital. If they haven't built a "Palace IV" when Renaissance starts, they suffer economic penalties and/or there will be no expansion stability increase. I guess everyone gets the picture: Palace must be according to age, with better palaces enabled on age-progressing. This enforced re-building of better seats of government equals gradual modernization and governmental reforms, and is not meant to replace disruptive civic switches. It forces the civs to regularly re-evaluate whether or not the capital is currently sitting at the right place. More modern palaces would have increased building costs, but also a larger bonus per age. In 1.15, it's always the same basic bonus (+1 happy +2 culture +4 espionage) which could be modified a little bit. If the slowly increasing bonus and/or the building name depend on the current civics, that is even better. This idea pretty much favors the industrial center of the nation as the best place to quickly build a palace.
- Major change for the administrative centers: On foreign continents, colonial maintenance costs are tripled unless an administrative center is present. Once per colonized continent, an administrative center can also be hammer-built, with half the cost on historical areas. Until an administrative center is built there, the government center (palace) cannot be moved to another continent. If combined with idea 1, this only affects colonial empires, I think.