Whether or not a culture was considered superior was posited as a reason some empires endured.
In the book the grand chessboard,
"Rome’s imperial power, however, was also derived from an important psychological reality. Civis Romanus sum—“I am a Roman citizen”—was the highest possible self-definition, a source of pride, and an aspiration for many. Eventually granted even to those not of Roman birth, the exalted status of the Roman citizen was an expression of cultural superiority that justified the imperial power’s sense of mission."
Recently, I came across a post questioning how China with its large population was able to unite itself into one nation, while Europe's history is marked with strife.
One of the reasons put forward by a top answer and relevant to this post, was their unifying culture. "China (or at least its core) had a central, unifying culture built around philosophers such as Confucius and Lao-tse that was attractive to people over a wide land area."
Somewhat echoed by the author of the book mentioned above, "That unity was reinforced, legitimated, and sustained—again, as in the case of Rome—by a strongly felt and deeply ingrained sense of cultural superiority that was augmented by Confucianism, an imperially expedient philosophy, with its stress on harmony, hierarchy, and discipline."