culture system is good regarding flips and ancient times-but tile ownership / ownership of land has nothing to do with the shortest distance to the oldest theatre, if more than one contestant claims the tile (and the legal/political system is stable enough)
i'm fine with cities flipping(would be possible in cyprus, also with the caused unhappiness) but just because the greeks have one theatre, they dont shift the border, which would be defined politically (overthrow situation are exceptional.)
why not reserve city places with forts?--they can be built rather late/ small maintenance fee would be possible.. [many cities started as forts, meaning just outposts that don't even compare to size one civcities]
Forts(can only be build on own land btw, which would mean that you need quite some for reserving a city a bit distant from you home..)/Outposts here also mean something like the "Hereby I claim this for [insert King here].." of the Colonial Age
Perhaps outposts shouldnt be allowed until, say, gunpowder.
The shift between culturally and politically defined borders isnt that easy, though (perhaps around Nationalism)