Greensleeves is almost 500 years old. I'm sure there were other very popular songs when it came out, but Greensleeves had to staying power to still be here. What do you think is today's Greensleeves?
Imo Greensoeeves mostly endured because it can be perfectly whistled by everyone and still be played by professional musicians in a way that awes the audience.
This will probably not be th reason why current songs will stay arround. If society doesn't break down, I assume that every popular melody, be it from the US, China or Lebanon, will stay around and get reused every ~30 years to grab some quick money.