Why was it so hard for Steppe empires to maintain their identity when conquering peoples outside of the Steppe?

Almost all steppe Empires had core populations in the hundreds of thousands with a highly mobilized population of warriors accounting for nearly all men of age to serve in their armies. This was achievable because nomadic people of the steppes are herders and herds can be maintained by minimal numbers of people. When these tribes became Empires they would effectively distribute all of their core male inhabitants throughout their empire, where they would then Marry many, many women of their conquered peoples. In Song China in 1120 had a population of 0ver 100 million people while probably diminished by the end of the Jin Song wars this population was immense as compared to the 100,000 or so Mongol soldiers that conquered it. These males most likely bringing limited numbers of their societies women with them had their children raised by foreigners, in a foreign land where they were the extreme minority. The Steppe Empires also came from societies often with no written language, limited legal codes and most importantly no urbanization. They stepped into complicated societies that demanded them to take on these issues or face complete collapse, as such they simply would build off of the systems and styles of the conquered to fit their needs. In this climate their own cultures were rapidly shed and they adopted those of the conquered.

Though there are some exception to what was said previously those Steppe culture that did maintain their cultural identities had one extremely important difference they brought their families and as such kept their culture intact. This was the Case with the Turks, and The Hungarians, but then again they didn't face the same demands of empire that the Mongols did.