Our world would be a $hithole devoid of resources capable of sustaining society. Look at the massive poverty in overpopulous countries like China or India or the entire continent of Africa.
Even if "overpopulous" were a real word, it would be difficult to define.
The entire continent of Africa has 1 billion inhabitants. It is 3 times the size of China, which has 30% more inhabitants yet has 70% less land.
China is also much wealthier than Africa, despite being much more crowded.Within America itself, some of the most crowded areas are the wealthiest (central New Jersey, southern Connecticut, southern California) while some of the most sparsely populated are the poorest (North Dakota, western Arkansas).
Your thesis doesn't really hold water.
It really comes down to culture more than population density.