Yeah, you're right on this. The main reason for this probably being that Mongols were what, 100K people ? They could never have imposed their kinda 'backwards' culture to Persians and Chineses.
But OTOH, Romans did not destroy conquered culture : the Gauls became Gallo-Romains, they still used to speak their native language, their ancient customs and so on. A lot of place in France are still called by their gallic names.