I agree that there absolutely should be
some incentive to change your empire's capital, at least for some civs. I mean, Rome is Rome, but even they changed their capital to Constantinople (centuries
before most historians consider the ERE to be Byzantine). Even in the Western Roman Empire you get regular capital changes to Ravenna and Milan, etc. And that's not to mention how many times China's center of government has moved over the millennia.
Perhaps there could be a bonus attached to certain governmental civics for moving your capital? Something like a bonus to

or

in the new capital for a certain number of turns, or a significant reduction to maintenance. Once the bonus elapses (after lasting 10-20 turns), each civ would have an incentive to build a new palace to restore the bonus. (Perhaps that could be a bonus attached to a civic like Bureaucracy?
I'd also suggest that the 'Palace' wonder be less expensive, so the production costs are less of a hindrance to moving your capital around.
One other possible incentive for moving your capital, might be wonders that have the palace as their prerequisite. There are quite a few wonders that might qualify, especially any royal tombs (Pyramids, Mausoleum of Halicarnassus, Taj Mahal, etc.) If such wonders were limited so only one could be built per palace, we might incentive moving the palace to clear up a fresh 'slot' for a new wonder.
Just spitballing here, but this might be part of a much more ambitious proposal, to expand the current Palace into an entire 'upgrade tree' -- adding quasi-national wonders like 'royal mint' ('national bank' for democratic civs), 'royal gardens' ('national mall'), 'royal tombs' ('national cemetery'), etc. Each building would be unlocked by certain techs, with more advanced buildings giving better benefits but being more expensive to build. When a new palace is built somewhere else, the new capital would be able to build any of the palace upgrades, but the old ones would remain and continue providing benefits to their city. This would provide an incentive to move the capital, while also providing a competing reason to keep it in a single city. It would also encourage civs to
not move their capitals once they hit the modern age, since they'd need to keep the palace in the same spot until they can finish the upgrade tree.