I think both the most common sides of the argument are at fault. I think Mongols should be in over Korea, though I'm Korean--partly because they made a huge world empire and suchlike. It always annoys me when I see other Koreans on internet forums with poor English (not to sound...ok it already sounds patronizing), but more importantly with a swollen sense of national pride.
Korea should be proud, but it certainly didn't FOUND all these other cultures or make Chinese characters, lol. I get the impression this desire to be first comes from Korea's long history of having had to deal with foreign invasions. Koreans defeated many foreign invasions, but they did succumb to Mongols and Manchus as well as the Han Chinese, though all of them were ousted in a few years, and the first major Japanese invasion was wiped out by guerrillas and Yi Sun Shin's naval expertise (though the Japanese did major damage to Korea in both its major invasions).
I do think Korea will be included in an expansion pack. It's all too easy to find a fluent Korean speaker who can speak in the old-style Korean now on some historical Korean dramas. People who look at the Seoul CS and say Korea wouldn't be in ought to look at Oslo and the Viking in the opening cinematic.
But yeah, Korea is a unique country and has contributed lasting cultural, scientific, religious and commercial influence into both China and Japan (though it did also, like each of them, receive influence from the others). King Sejong should be the leader imo. I'm tired of Wang Kon, Taejo and the like. Sejong is the king Koreans most respect, and he created the Hangul alphabet, drove out the Wokou Japanese pirates, made some fearful military machines, and fostered scientific and artistic innovations (among them a celestial globe and a unique musical instruments).
The idea that Korea hasn't had lasting impact beyond its borders is false. Koryo celadon pottery, Digital Multimedia Broadcasting (which Korea did actually invent:
http://en.wikipedia.org/wiki/Digital_Multimedia_Broadcasting). Potters in Japan, stolen during the Imjin Wars. The first observatory in world history (still standing at Gyeongju), sends the 3rd largest number of Christian missionaries overseas annually, behind Britain and the United States--might have surpassed Britain at this point, and of course its exports of computers, TVs etc are fairly popular. Samsung is a Korean company, not a Japanese one.
Here are my ideas for a Korean civ. =)
Leader: King Sejong. Strong defensive army, likes to trade, doesn't expand much. Emphasizes science and culture.
UA: Morning Calm (could be any of the following: Cities within 2 tiles of hills and mountains receive +5 defense, +3 science and double hitpoints....or, Ranged units +1 range and +2 line of sight, citadels do 1 extra damage, cities doubled in hitpoints...or anything vaguely commercial, scientific and/or primarily defensive...Cities +3 science and culture when not at war? maybe. OR--Every Social Policy that is unlocked grants you +X beakers, and can overflow to the next technology you research)
UU: Hwacha, replaces Trebuchet. Costs more and moves slower than trebuchet, but can do splash damage to multiple troops. Splash damage increased in range and damage when on hills or fortified. Extra defense against infantry. (Hwarang would be a nice alternative, but we already have too many archer replacements)
UB: Seowon (University that adds +1 culture, costs +1 maintenance, and provides +65% science rather than 50%, or maybe a univ which adds 1 hammer or suchlike).