Don't know about cheapiness but instant noodles are fast to eat. Even here in Finland instant noodles are pretty much a must have in every kitchen. And let's face it - the taste is amazing ! While I was in Korea for few weeks in 2016 I didn't eat instant noodles that much but the taste was much better and portions were much bigger than what I'm used to in Finland.
Didn't really answer your question but I actually think it's only because it's so fast. If you have noodles at home would you go your way to actually go to a restaurant or cook for yourself or just boil water and wait for 2 mins and eat while you do your work/study etc.
(And just to add - if Finland had places that had cheap, amazing and 24/7 food I'd go for it all the time. But unfortunately I live in Finland and everything is super expensive, tasteless and closes early)