It was one of the first democratic governments in recorded history. Letting people vote on leaders was revolutionary at the time and did lead to things like the roman republic, the american revolution, and the french revolution. It lead to a lot of time being spent on the tragedy of being human or self aware. Which of course lead to things like maybe i deserve to have a say in the government.
Later when the Romans took over they looked at all the Greeks stuff and thought huh? maybe this is a good idea. And the rest of course is history.
The Catholic church had more influence because of the location of the Vatican it is in the south so the priest would travel mostly around the south to spread the word of God.