While I don't personally know why or when the Blue Raspberry flavor became popular, it's important to note that blue raspberries are indeed a real fruit, native to North America, that the flavor is based on, so the flavor has just as much of a "real" basis as banana, lime, etc.

Blue raspberry is a real fruit. The basic reason it's so popular in artificially flavored or colored foods is because there are a lot of red-ish common flavorings (watermelon, cherry, raspberry, strawberry, etc.) But the desire with artificially colored foods is to have a distinctive color palette, so blue raspberry becomes more common than red raspberry.