Actually, the very idea of large-Empire stasis is itself a misguided trope. The Roman Empire, for instance, was not simply an unchanging blob. Even after Augustus, when the transition to Empire was largely completed, structural, organizational, economic, and political changes were many. To name a few, there were the gradual shift from silver to gold coins, Diocletian’s political overhauls (tetrarchy and division of local administrative units), and disbanding of the Praetorian Guard. This is not to mention the changes that more natural forces, such as the Antonine/Cyprian plagues, caused the Romans.
The idea of a non-changing and continuous “China” is itself also misguided. From the Han Empire onwards, one can count literally hundreds of Kingdoms, Empires, and principalities that claimed to succeed the Han, including many very “barbarian” Polities (such as Northern Wei, Northern Qi, etc.; indeed, Sui and Tang can be seen as at least semi-barbarian regimes). Leaving aside succession and cultural legacy, and even looking at the period from Song to Qing, we can see immense change in almost every area of life. Religion evolved from predominantly Buddhism to a battle between Buddhism and Daoism (and the evolution of the Dao-Xue school in the Southern Song) and the gradual rise and ascendancy of Neo-Confucianism in the Song to Ming. We see the evolution of organizational structures, from the bureaucracy of the Northern Song to the clerical bureaucracy of the Southern Song to the appanages of the Yuan to the autocracy of the Ming. We see the evolution of commerce and economic policy (the Southern Song developed the first standing navy in the world, the Yuan used the Song fleet to force the nominal submission of governments from Dai Viet to the straits of Malacca, and the Ming sent out one of the grandest naval missions in history, before ultimately so retreating from the coast that pirates took to the seas trade was conducted often at their discretion.
I could go on, of course, but the point is: even seemingly eternal space-filling Empires change. It’s just that it’s not always apparent to the naked eye.