Yeah, the Japan transition problem (nopenopenope) is the biggest obstacle I see to no modern Korea. On the flip side, that Exp-Spain is called Spain and not Castille is a pretty strong sign that not having all civs that exist today have a modern version is, in fact, by design, and I think we fans had better prepare ourselves for more of it. There *will* be modern day countries that exist as exploration or ancient civ and have no modern version. Meaning you, Portugal and Greece.
Given the transitional difficulties (see again: Japan nope nope nope, and especially Meiji Japan), I think it's pretty plausible Korea avoid that fate. But the desire of every modern country to be able to play their civ to the end of the game will, I think, certainly go unmet.
I wouldn't sleep on the possibility of Exp-Joseon and the modern civ being simoly called Korea, though (representing, in that case, both late Joseon when the name Korea started gaining traction, resistance to Japan, and modern Korean civilization).. People want to read a rule that a civ that uses some dynasties or period names will always do so, but I'm not convinced. I think when that civ name is particularly associated with an era in (western) consciousness, it's plausible, even pretty likely that the civ name will be used for that era and dynasty names for the other eras. Persia-Sassanid-Safavid is a progression that I could very well beliueve happening. Same for Axum-Solomonid-Ethiopia. I don't think there's hard and fast rules for naming patterns - just trying to figure out what work best to fit the era system while makign the names reasonably distincts and reasonably recognizable. Likewise with the idea that because the end civ are Mughal and Qing, no modern names can be used (nevermind that most currently existing European civs use modern names or shorthand thereof). There's a great deal of complication in which names go where.