Unity allows easy spreading of disease and corruption, cancer cannot spread between different people. If a union in one country is corrupt, it won't automatically affect the unions in another country.
China was a united entity against the mongol invasion, didn't work out very well, because you take out the center, the rest collapses.
Europe was deeply divided, and just because your neighbouring castle surrendered, doesn't mean you will. Because you are the local noble who owns the land, rather than some bureaucrat employed by a distant emperor.
I'm not sure what 'entire history of war' you are reading. Did you only read 19th century history or something?
If large empires always had an advantage, then you would see endless snowballing, and only end up with mega-empire-blobs, and one-world-government.
That is not the case. You have period of imperial blobbing, and also period of intense fracturing. Europe fractured after Rome, because smaller polities were much easier to maintain, with fewer layers of bureaucracy to feed.
The small Frank kingdom (that only owned half of France) was able to fend off the great Jihad from the Umayyads that had crushed the Visigothic Spain. Whereas if you took out Rome, or the Chang-An of China, the rest of the empire would be paralyzed and unable to act.
Unity allows easy spreading of disease and corruption, cancer cannot spread between different people. If a union in one country is corrupt, it won't automatically affect the unions in another country.
China was a united entity against the mongol invasion, didn't work out very well, because you take out the center, the rest collapses.
Europe was deeply divided, and just because your neighbouring castle surrendered, doesn't mean you will. Because you are the local noble who owns the land, rather than some bureaucrat employed by a distant emperor.