So, using agile approach here might work?

If the goal is to serve people with larger distances to groceries today, and unmet needs, it's probably not as helpful in wealthier areas like Staten Island. Though surely some people there will benefit.

I can't find easy data on grocery store density, but I'm guessing if the program is as successful as it seems like it should be, dozens of stores across NYC seems like a place they could get quickly. Probably not evenly distributed across boroughs though.

The stores aren't supposed to replace the existing stores or serve the whole city population. They're supposed to put some outlets into underserved neighborhoods whose residents now have to subsist on junk food or else use transit for basic groceries.

If the goal is universal grocery availability at the lowest prices, then I agree: this plan alone won't achieve that. However, I see a couple of factors here with the plan that could achieve some measures of success.

The first is that the plan is to place these stores in, essentially, food deserts in the city. That would have an immediate positive impact on grocery availability for the localities around the 5 stores. Further, the fact that the city stores will be selling at wholesale will mean that food prices at these could be noticeably cheaper. This would steel customers from other grocery stores, forcing them to lower prices to attract their customers back. While grocery stores usually run on small profit margins, that usually is still while having to pay property taxes (which city grocery won't), but land (which city grocery won't), and pay for expensive business operations (marketing, executives, etc) (which city grocery won't).

I'll be the first to say its not a slam dunk win for everyone in the whole city immediately, but the locals around the store benefit immediately, and the success of an alternative without a profit motive puts pricing pressure on existing stores possibly fleecing customers with higher prices.

Oh, well if that's the primary goal - to eliminate food deserts - then hell yeah. Makes total sense