Do you have any evidence to support that opinion?
Since you mention ancient Greece, there was no such thing as Greek Democracy. There was only Athenian Democracy, and it was only a partial democracy by the modern definition as to qualify as a voter one had to be an adult male Athenian citizens who had completed their military training as ephebes. Athenians of foreign origin, even if they had been living there for numerous generations, were excluded. Furthermore Athenians practised slavery, which is against the fundamental understanding of democracy today. All in all that meant that only 30 percent of the total adult population was eligible. That was therefore a system intermediary between oligarchy and democracy, like that of the Roman Republic.
Of the hundreds of Greek city-states and colonies ranging geographically from Spain to Ukraine, it is telling that (partial) democracy was only able to develop in Athens, the richest of all the Greek cities, and only during its golden age.
Regarding the Roman Republic, it was originally an oligarchy in which the patrician class monopolised most of the political offices. As the republic grew wealthier, the plebeians started to demand equal rights, leading to the
Conflict of the Orders. It ended with the promulgation of the
lex Hortensia in 287 BCE, which conferred nearly equal rights to the plebeians and patricians. That was when Rome already controlled most of Central and South Italy.
At least 7
academic studies have tried to estimate the GDP per capita in ancient Rome. It ranged from $500 to $1000 in
1990 Int$. That was the average for the empire, but the GDP per capita was 40 to 66% higher in Italy itself. Rome was of course the wealthiest, and it is reasonable to assume that Roman citizens in Rome were at least 2 or 3 times richer in average than in other Italian cities (once slaves, liberti and foreigners are excluded). That would bring their GDP per capita around $4,000.
As I mention the topic of slavery, it would be more logical to consider that the United States only became a modern democracy when slavery was abolished (in 1865), or even when Black people obtained the right to vote (in 1870). In 1870 the GDP per capita of the USA was $3,736, very close to the $4,000 to 7,000 range of other democracies.
As for Albania, it became a democracy in 1991 when the GDP per capita was $4,454. It also fits the model.