This is one of those odd questions - regarding why folklore selects one character from history and not another. Certain factors need to be present, certainly, to justify the association of a notable from the past to become the subject of a motif. And then once that selection is made, it has a way of discouraging the association of the motif with others in the neighborhood: we can't have every Holy Roman Emperor slumbering about waiting to awaken, now can we?

In my Introduction to Folklore I describe a variety of "legendary characters similar to condemned souls," (condemned souls being a distinct type of supernatural entity). These include the Wild Hunt, the Flying Dutchman, the Wandering Jew, the Will-'o-wisp, the community that has sunk beneath the ground or the waves only to resurface briefly every century, and the sleeping king and his army.

About this group, I write the following: "Europeans were fascinated by the idea of condemned souls, either of individuals or groups of people, who could not find rest. These unfortunates were forced to exist in a nether world, appearing occasionally before the living as evidence of their hideous or peculiar plight. Such motifs have been favorites with artists and writers."

And specifically about the sleeping king and his army: "The “Sleeping Army” is a motif that appears in a variety of stories telling of a group of warriors killed in combat, who haunt the battlefield or wait inside a mound for some future conflict. People often believe such an army serves as a matter of last resort, a supernatural force that will rise up if their country is threatened with destruction. King Arthur’s knights are often regarded as sleeping in this way, waiting for the return of their king, healed from his wounds after recuperating in the western island of Avalon."

It would be a worthwhile research project to pursue the question about why this character from history but not that one, became the focus of oral tradition. I have seen this question addressed in other contexts, and too often the answer is a simple shrug of the shoulders, because it merely unfolded that way for little obvious reason. Certainly, the folk perceived Frederick Barbarossa to be the right of monarch for the job, so he came to own the motif, and at the same time, that adoption shoved away any competition.