I agree with most of your post, but I think that $2-$3 a person is probably optimistic. I regularly manage about $5.50/meal, but less than that involves cutting back in quality or selection.
These are your most expensive ingredients in NYC today in a non-upscale ( and non-ethnic ) supermarkets. At best you are getting 1/4lb per portion. All other ingredients would barely make a dollar if you don't buy a precious single onion and instead buy a bag of onions or instead of getting a single carrot, you buy a small bags of carrots.
Obviously you don't buy salmon when it is $16/lb as you know that at some point over next few weeks it would be $11/lb. The last one that I got at Chelsea market was $9.99/lb because they did not correctly predict how many were going to be bought as fillets and sushi so they wanted to offload the last two at the end of the day before getting another 10 next morning.
BA cost of raw ingredients is at best 5-10% better than yours when you walk into a random supermarket and just buy non-insanely priced items.
I've cooked and bought groceries in NYC several times and while the prices are definitely competitive with some hunting, the 99c whole chicken I found was total garbage and basically was like water and salt.
My step-dad used to swear he couldn't tell a difference between the $1.99 special chicken and the regular stuff I bought that was $4 - 6.99. To me the $1.99 tastes like eating saline solution (I've had saline injections, it tasted like that to me). Maybe it's just a question of taste.