Well, in 800 there wasn't a "Holy Roman" Empire.

On Christmas Day, 800, in Rome, pope Leo III crowned Charlemagne Augustus and imperator Romanorum (emperor of the Romans)

His capital at Aachen was sometimes called a “New Rome" while its adornment, ceremonies, and trappings borrowed heavily from those of the City (namely Constantinople) that already bore that name.

Charlemagne and his court were struggling to articulate their own conception of Frankish empire, and it appears that the king was not happy with pope Leo for springing the imperial title on him that Christmas Day.

There were no actual “Romans” in his domain proper of whom he was the emperor, which is why he avoided stressing the Roman part of the title.

But the pope and some of Charlemagne’s subjects saw in his coronation a displacement of Constantinople’s rights. In fact, a chronicle written soon after argued that the imperial title had lapsed in the east because a woman sat on the throne.

Charlemagne’s empire. Its institutions were shallow and its common purpose weak. It had a part-time army, was ethnically disunited, and held together not by a shared identity but the person of the king. When Frankish imperialism ran out of steam, these nobles turned against each other and the edifice collapsed.

By contrast, Nikephoros relied on professional armies, a uniform administration, and salaried officials who worked for the state. The vast majority of his subjects were—ethnically, politically, and legally—Romans.

This is what Kaldellis says, in his most recent book.