> And they don't eat much of the vegetables, because they are expensive and hard to come by
Nearly everything you said is incorrect, this one in particular. Vegetables are not expensive in the US compared to other nations of similar incomes.
The US is a leading producer of vegetables such as cauliflower, lettuce, spinach, broccoli, squash, potatoes (/tuber), onions, turnips, soybeans, carrots, pumpkins and tomatoes (/fruit). Globally the US is third in vegetable production, behind China and India. For one example, the US produces about 15% of all lettuce globally (with 4% of the world population). Vegetables are more than plentiful in the US, we unfortunately waste enormous amounts of vegetables.
The US consumes more vegetables per capita than these European nations:
Germany, UK, France, Switzerland, Sweden, Finland, Norway, Russia, Austria, Ireland, Iceland, Hungary, Czech, Bulgaria
US vegetable consumption is almost identical to the average of the EU. It's also essentially identical to the consumption in Canada, New Zealand and Australia.
Interesting fact: the poorest countries in Europe typically consume 50% to 100% more vegetables per capita than the wealthiest countries in Europe.
Source: FAOStat