This negates the fact that if the war was secret nobody would even know Khan existed let alone three hundred years later. He needs to be infamous. In order for Khan to work he must have a lasting and persistent presence in history like Hitler. "Never again!"
When Khan (who was the most famous of them all) seized power in India in the early '90's, he became known for doing so; the others (Randy Morrison, Chen Tijun, Arcturus, etc.) less so since one was a typical right-wing American survivalist with a bunch of like-minded wackos in Florida, another being a group of neo-Amazons on their own island (Chen even wears body armor), and the third-mentioned one is the head of a global space cult similar to the cult that killed themselves in order to go into space by dying (the one that Nichelle Nicols's brother was a member of.) Khan simply had more resources to do what he wanted since he controlled half of India and Asia, and had even built a submarine fleet and a arsenal of missiles. The war itself is seen by historians from the future as being one, but not perceived by the people of the '90's as being a big conflict, rather just seen as part of the conflicts and events of the time, according to (Greg) Cox.