Final answer:
The Greek system fell due to internal conflicts and stratification, frequent governmental changes, and external conquest, not one government system's permanent rule.
Step-by-step explanation:
The downfall of the Greek system of government was not due to one particular system taking over permanently, but more due to frequent conflicts and stratification within and between the city-states, and eventual external domination. The Greek city-states, known as polii, featured various forms of government including tyranny, aristocracy, oligarchy, democracy and others that could change over time, which may have contributed to instability. Additionally, Greek society faced the challenges of class divisions, societal stratification, and external threats, such as the Persians and later the Romans, which overshadowed their innovative political experiments. The ultimate downfall came when Greece became too geopolitically significant to remain independent because of its strategic location and extensive trade networks, resulting in it falling under the influence or control of larger powers.