I am in the Northeast, one of the most expensive parts of the country.
Reliably, onions, potatoes, cabbage, winter squash and bananas are to be had at less than a dollar a pound.
Frozen spinach and peas and fresh asparagus and grapes on sale, a dollar a pound. In season, apples and zukes and green beans and summer squash are a dollar a pound.
In season, lettuce is a dollar to two a pound. In two pound bags, fresh kale and collard greens are available year-round for two dollars a pound. Go to an ethnic market (e.g., Hispanic or Chinese or Indian) and prices are at least as good, sometimes better.
At 80 I have some mobility problems. I have been driven to some ethnic markets in the suburbs and found good prices. However those near where I live only carry grains and beans, seeds and other non perishables. Since I am trying to loose weight (successfully) by a very low carb diet, most of what they sell cannot be used by me until I have lost 20 pounds, and then only in modest amounts. Also I cannot eat the potatoes, winter squash or bananas for the carbs, and onions are a relish, not a main course. I have been using a fair amount of cabbage. Once or twice this year some grapes have been 99c, but a bargain is $1.99 and usually they are higher. I have also seen fresh asparagus sometimes as low as $1.99 Frozen veggies are rarely a dollar unless it is the 8 or 12 oz packages. I did see fresh carrots for $1 a pound today. So your advice may help some, but where I live it does not tell the story.