The mystique of the Ace Pilot has been around as long as there have been airplanes used for combat. Aces likely got their start in the popular imagination through a combination of newspapers and the fact that they were few and easily recognisable. According to The Other Wiki, the majority of victories in aerial combat during World War I were won by about 5% of all pilots and these pilots were honoured highly, receiving major publicity to boost morale at home. The Germans in particular had a very exacting standard for confirming kills and the requirements to earn their highest award for gallantry actually went up as the war went on. Only in France and the US were they really called aces; the British actually used the term "star turn" to describe them, a showbiz term for the featured show or performer in a theatre.
It may be a cultural thing as well with a lot of the Ace Pilot mystique coming from Europe and the US, where planes were first invented. The sky is a big thing for us in the West. Quick, think of a bird. Any bird. What's the first thing that comes to mind? It was most likely something like "beauty" or "freedom". Now think of a bird of prey. You'd probably get something like "sleek" or "graceful" or "deadly". We have a very romantic image of things that fly. During the war both sides printed a lot of propaganda to boost morale in the trenches, including one piece about a group of angels that supposedly appeared to save a group of British soldiers that were about to be overrun. Also unique to Europe was the idea of the Knight in Shining Armor, which may also have played a part in shaping the imagery of the Ace Pilot as some kind of "sky knight". Popular imagination at the time held that there was something almost gentlemanly about air combat and the aces on various sides of the war developed a sort of professional rivalry with one another.
When the war was over, aces still found work as part of unofficial units fighting on different sides in civil wars, in places like Spain and China. The idea of the Ace Pilot most likely spread from there to Japan through American and German sources. It also helped that air power would play an important part of basically any major conflict from that point until the modern era. The Battle of Britain. Pearl Harbor. Dresden. Midway. Hiroshima and Nagasaki. Both the greatest and most terrible moments of World War II involved aircraft of some kind, although naturally fighter pilots continued to be more glamorous than bomber pilots. In the Pacific, the Aircraft Carrier was the weapon of choice, eventually pushing the Battleship the way of the Dodo. The infamous Japanese suicide pilots were called kamikaze, most often translated as the Divine Wind in reference to a typhoon that wiped out a Mongolian fleet trying to invade Japan way back in ancient times. In other words, a miracle that would turn the tide against the Americans.
It isn't just fighters that have helped build this image. It's doubtful that anyone will forget the iconic image in Apocalypse Now of helicopters and Wagner. Orchestral Bombing is also its own trope, demonstrating the power of air power in the public imagination. The reason why people switched to guerilla warfare when they wanted to win is precisely because of things like air power - if they stuck their heads out in the open they would be vaporised in an instant, so they don't. Even if air forces around the world don't encourage this image they do nothing to discourage it and to this day the major world powers maintain aerial demonstration teams drawn from their air forces - the Thunderbirds (USAF), Blue Angels (US Navy), Russian Knights (Russian Air Force) and so on. Military aviation is now a multi-billion dollar industry and big countries throw good money after bad into the black holes that are fighter development projects so that they can have the best toys.
In short, all of military history for the 20th and 21st centuries has culminated in the creation of Ace Combat. Think of that what you will.