Biologist
Emperor
So far I've never felt a need to move my capital city. I suppose it might make sense if the capital ends up way on the fringes of the empire somehow, or maybe if you want to take advantage of a larger boost from resources (since the capital often gets a smaller bonus than other cities from resources)? That seems like a very advanced move though in that you'd have to calculate in advance without seeing projected outputs how many yields you'd be gaining from switching. I suppose you could also move the capital away from potential military threat, but since capitals are no longer central to military victory and military units return to their own corners at the start of each new era, that doesn't seem too useful.