Although others may disagree, it seems that the success of "democracy" and "republican government" in places like Greece and Rome were do to special local factors that mostly did not exist in China.
Greece and ancient Rome were both hilly countries, which is to say poor for mass production of food using slave labor. With some other benefits of temperature and soil, they were good for producing delicate, high value-added crops like grapes (for wine) and olives (for oil) that are much more suitable for cultivation by "free" labor. In such a situation, one man was about as good as another, hence the idea of one (free) man, one vote.
The hills also made it harder for a central government to collect taxes, and easy for local-citizen armies to defeat much larger invading forces. Their relative wealth gave the peasants a strong incentive to enlist in such armies. Finally, the above mentioned goods were shipped around the Mediterranean by sea, far from land (and central government control).
Few of these conditions existed in China. The land was relatively flat, and subject to periodic invasions by northern hordes that local levies could not defeat. Only a strong central government (and army) could protect the people and engage in projects such as the Great Wall, that slowed down, but did not totally prevent such depredations. The one high value-added agricultural product, silk, was shipped by land, not be sea, and therefore did not foster "democratic" traditions that way that grapes and olives did.
Rome ceased being a Republic and became an Empire when a series of successful wars reduced foreign markets for wine and oil, and increased demand for (slave produced) grain from newly conquered territories such as Sicily. Essentially, Republican Rome fell when its best "clients" did.
It's probably not a coincidence that in Europe, the freest people lived in mountains (the Swiss), an island (England), or some peninsular combination of thew two (Rome and Greece). Likewise the freest parts of China were Tibet (until recently) and Taiwan, an island.