I mostly agree with what you say, but:
> People could eat relatively healthy if they wanted to, but they don't. [emphasis added]
It's not an issue of want. I've lived in a near food desert. I was in a relatively well-off part of a very poor part of town (many people lived without cars, high unemployment, etc.). The local grocer had god awful meat and produce (produce would spoil in 1-2 days of purchase, meat wasn't much better). To get good food I'd drive sometimes 10+ miles away and get, for the same list price, much better quality meat and vegetables. I wasn't breaking the bank, but I had access to a vehicle and the time to take to go make the purchase (the local grocer was only good, for me, for staples like dried beans, rice, and flour). The others living nearby without a car, or without the time/money to dedicate to that extra trip for groceries had to subsist on what was available locally, which meant often some very poor quality foods (with regard to health outcomes at least).
Otherwise, I agree that good food is not expensive. I saved money and got healthier by spending less on food (chicken breast and ground beef at $2-3/pound, catch on sale days and freeze; rice and beans cost maybe $10/month as a single adult; a few key vegetables and fruits cost $5-10/week).