Athens had direct democracy for a while, except in time of crisis, when they voted power to a strongman. It did not work above the city-state level, and not well there. The PATRICIAN class practiced "democracy". The slaves (lot's of slaves) and to some extent the peons (forgot the name for the common folk) did not participate.
I guess you could get it to work in a pagan culture if it was on the level of a city state (can't degenerate into pork hunting for separate regions, highly homogeneous voter) and only the most responsible quarter of your population did the voting.
Your Roman example boosts my case even more. It degenrated into Emperors who demanded worship like a god in a relatively short time after it expanded out of Rome itself.
Your two poor examples from over a thousand years ago bolster my case rather than refute it. Without a Judeo-Christian world view, self government is very difficult if not impossible to sustain.
Without the Judeo-Christian worldview, which has a direct bearing on politics in this country, there would be no FR.