Athens established a government based on democratic principles. However, I believe there is a series of reasons for such an establishment far from relieving social strain. You have rightly stated that due to the emergence of maritime trade in Attica, the Aristocrats became wealthy and had control over the Athenian government and the people. I believe such control was more eminent with the Roman Republic.
Originally, Rome was a city-state like Athens and rapidly expanded beyond its borders to incorporate the entire Mediterranean world. The Roman Republic, founded in 509 BCE was under the governance of representative officials, conversely, Athenian democratic rule rooted around the 5th century BCE was limited to the city of Athens and its periphery. While many countries looked to the Romans in developing their democracies, the Roman Republic although constitutionally democratic, was fundamentally undemocratic in practice. A select cast of wealthy aristocrats dominated the Roman Republic. When comparing the two democracies, the Roman Republic was less democratic allowing the citizens to vote for their representatives while at the same time, putting more value on the votes from the rich. On the other hand, Athenian democracy allowed for greater civic engagement by ensuring the citizens voted on legislation and bills by themselves. For example, it allowed men over 20 years to adequately getting involved in all levels of government.