You've still got the Mongolians and, if they're doing it right, a collapsed barbarian/independant China to worry in any case.
Still, I've already agreed that my UP is not the best, but it is possible for a UP to have nothing or very little to do with the outcome of the UHVs. Playing Carthage, I never needed the cheaper mercenaries, and playing Babylon, I've never gone and captured other cities.
I think having three cities in Manchuria would indeed be pretty unchallenging. The thing is that the three silk ideas make for a very interesting early game, because you either have to become really chummy with China, or you have to go and found a colony in what's considered China's territorry (which is not that ahistorical per se, just to do so in south China is).
I did think about invading Japan as a third goal too, but I felt that the historical invasions were really much more the Mongolian doing than a genuine Korean "project". Seeing that all the eastern Asian powers are practically bound to declare war to Korea sooner or later makes keeping the cities pretty interesting.
