I'm being snarky because your criticism of the tool, and its data sources, is a weird form of nut-picking.
You're able to purchase groceries for your family, for your diet, in your locality, from your available stores, for less than the stated average.
You think the diet should be different, and blame "society!" for the nutrition goals not resulting in a lower budget.
This is not a serious criticism. It is an unverifiable anecdote coupled with generic contrarianism.
The fact some people spend more or less on groceries is already factored into the data, as it's an average of prices. Averages are imperfect. The fact it's an average of prices (instead of spending) makes it slightly better, but anecdotal data doesn't meaningfully contribute to a discussion about it.
The diet, too, is probably imperfect, but the tool needed to normalize costs, not assemble a Costco rice-and-beans nutritionally complete diet to minimize costs.
So I have absolutely no idea what point you're trying to make beyond "I like to sound smart."