There are several reasons, but I'll explain what I think are the most relevant.

First of all, the music industry in Korea is structured very differently from its American equivalent. Until the early 1990s, South Korea was ruled by a string of pro-American dictators who were in many ways no better than the Kim dynasty of North Korea. With the democratization of the Korean government came artistic freedom as well. Suddenly, you had a big void in terms of music, but you had a population already rich enough to all own TVs and you had the money necessary to produce quality acts. However, there were no big agencies to manage artistic talent, which could now be developed freely.

As a result, there was an initial explosion of artists who developed and worked on their own. However, it didn't take long for a few of them who had business sense as well to realize that this process could be optimized through the creation of talent management agencies. The biggest agencies in K-pop these days include SM Entertainment, founded by Lee Soo-man in 1995, YG Entertainment, founded by Yang Hyun-Seok in 1998, and JYP Entertainment, founded by Park Jin-Young in 1997. They were able to perform a rapid landgrab that led to their dominance in the K-pop industry.

Lee, Yang, and Park all proceeded to apply the Henry Ford model to musical talent development. They would use their own fame and success to draw in middle school and high school age children through auditions. Remember that 20% of South Korea's population resides in one city (Seoul). Seoul is the financial, industrial, entertainment, and political capital of South Korea. Everyone wants to be in Seoul. So they held regular auditions in Seoul to find new talent (nowadays they are held in cities across South Korea on an almost weekly basis). This made it very easy to draw in the children, who were then placed in intensive training programs. The parents were eager to send their children to these programs, because everything was guaranteed for them - food, shelter, education - for free. The children would live in dorms provided by the agency, seeing their families only during holidays.

The "trainee" model of talent development is one of South Korea's big innovations (if you can call it that) in the entertainment industry. A large number of children enter entertainment agencies as trainees, but the process is very long (it can be 5+ years), and many trainees drop out. The trainees are not only taught how to sing - they also learn how to dance, act, appear on TV programs, and how to live life in general as a respectable entertainer. Whereas a singer in America can say all kinds of stupid and crazy shit and still be respected for his/her musical abilities, that would never fly in Korea. Polity is paramount and breaking social norms is a death sentence. Many agencies place "dating bans" on artists, not allowing them to have romantic relationships, because many of their fans see them as the ideal man or woman. This is also something that doesn't exist (at least not to the same degree) in America.

In any case, those who persevere with the training are generally able to "debut", sometimes as an individual singer, but usually in a group. Back in the 1990s, boy bands and girl groups were very popular in America. They went out of fashion in the US around the turn of the millenium, but that never happened in Korea. The Korean agencies persisted with that model to great success. This can be considered one of the minor reasons why finding success in America these days would be difficult.

However, the single biggest issue is that in all the training that I've described so far, one major component has been conspicuously absent - the trainees' creative abilities were not nurtured at all. This is entirely intentional. It was never the goal of the talent agencies to develop independent singers (this is part of the reason for creating groups instead of individual singers) - they want the artists to stay with them forever, so they can take a (large) cut of their paychecks. What you get as a result is a musical act that is put together by piecemeal - you have artists, song writers, composers, dance coreographers, costume designers, etc. all working together to create an act (although only the artists actually achieve any fame). No one is going to rock the boat because they know they are a replaceable cog in a giant machine. As a result, the music that comes out of the K-pop industry sounds very manufactured - you never get a single, driving vision. Instead, each "cog" has to come up with something generic and the overall outcome is rather bland pop.

However, there has to be something good about all this, right? Because K-pop has proven very successful across Asia. The reason for that is that shared Asian cultural values of things like respect, familial values, social conservatism, etc. make the K-pop model very palatable. Whereas American artists are notorious for doing drugs, having children outside of wedlock, going to jail, etc., K-pop artists would never do this (well, a few have, and they've been crucified for it). Basically, K-pop has taken American pop music and made it acceptable in Asia.

But America is different - we like bad boys/girls, and we don't care about (or even relish) an artist's personal life if they make good music. The same is largely true of Europe - the Beatles did loads of drugs, but they were loved across the European continent. K-pop has not succeeded over there either. You'll notice that Psy (the artist behind Gangnam Style) wrote his own music and lyrics - this is the sort of thing that is essential for success in America. Sure, there's Justin Bieber and other pop starlets who feel very manufactured, but they are oft maligned and only liked by a very small segment, primarily preteens.

The second major reason is that Koreans are Asian, and Asians are just not seen as cool in America. How many Asian-American sports players are out there? What about politicians? Actors? Musicians? Asians as a group are more highly educated than any other ethnic group in America (even whites), and the stereotype of the Asian nerd is very strong. We like to view our musicians as sex symbols, and an Asian male will never be seen as a sex symbol in America. With the exception of the stereotypically asexual kung-fu master, Asian males are seen as highly effeminate (see the differences in intermarriage rates between Asian males/white females and Asian females/white males for statistical proof of this). Psy succeeded because he's a fat, funny guy - the one case where it's OK not to be a sex symbol as a musician. A sexy Asian female might have success, but only within the context of strong fetishism by American men. But when not a single Asian-American male or female has seen any success, I wouldn't hold my breath for any foreign Asian artists.

You also have to remember that long-term success in America requires a solid grasp of English. Whereas other countries are willing to tolerate a lack of fluency in their native language, Americans speak English, the global lingua franca. We don't listen to people in other languages - they learn English so they can talk to us. The Korean education system, which is rooted in Confucian principles of rote memorization, has been a complete failure at teaching English. Most K-pop stars are far from fluent in English, the last nail in the coffin for K-pop success in America.