One of my favorite websites, Priceonomics, posted how the push from the Korean government made Kimchi more famous and accepted. It is true that Korean food has been heavily promoted. Growing up as a diplomat’s kid, I always saw my family promote Korean food. But I always thought that we were pushing too much. If it is delicious, people will eat it. I don’t remember Mexico pushing its cuisine but it is super popular in the US. I don’t remember Japan pushing Japanese ramen but it became quite popular. I believe that markets are efficient and eventually delicious cuisines are found and become enjoyed by everybody.
In terms of Kimchi and other Korean food becoming popular, I am sure that Korea’s strong push of Korean food (Do You know Kimchi?) played a role. But I believe that there were two trends that made Korean food become much more popular. First, K-Pop and K-Drama became quite popular around the world. I remember my father showing pictures of young girl fans in Latin America going crazy over Korean stars. I was also shocked when Americans started dancing to some Korean tunes. I thought hmmm…I have not seen this before. And then there was Gangnam style that was a real revolution. Suddenly everything Korean became so interesting and in demand. That really set the course. So rather than government policy, I believe that the popularity of K-content lead the way to the popularization of Korean food.
Second, the hipster movement and quest for authenticity. I used to watch YouTube a lot because I would sit in front of the computer all day long. After coding and waiting for results or when I wanted to slack off, YouTube was always there. I particularly liked cooking and food videos because when you are super stressed you become very primitive. Initially, I saw some chefs put Kimchi as a condiment to some dishes. Then I saw more restaurants talk about Korean food ingredients. And soon we had a wave of hipsters talk about Korean food and Korean culture. I live in K-Town and I can tell you that there are more Americans and foreigners in K-Town than before. There was a time that some restaurants had no English menus because only few non-Koreans visited them. Few restaurants were even surprised and shocked when a non-Korean walked in. Once I even had to help with the translation. Now you see much more non-Koreans in K-Town. Also, now most restaurants have English menus ^^
Overall, yes, the Korean government played some role with the spreading of Korean food but K-content and the recent hipster culture and quest for authenticity probably contributed more to popularity of Korean food.