Food delivery is nearly impossible to pull off, because you need to own the entire delivery chain in order to make money off of it. Instacart attempts to leverage existing chains around it, but then the prices are doubly marked up so no one wants to buy things, and replacing entire delivery-chain competitors in these highly ingrained markets is next to impossible.

The only kind of direct-to-home food delivery that will exist for the time being is the kind offered by the stores (because they make plenty of money on the goods they sell already, so they can offer delivery as a sort of perk), or a kind of luxury food delivery (in the vein of Blue Apron or, to a lesser degree, Instacart).

tl;dr: Blue Apron/Instacart, the "luxury" food delivery services, are the only non-chain delivery services that will survive. Stop&Shop Peapod et al. are subsidized and thus don't even need to worry about it.

Source: tried to start a food delivery startup, stopped when the math didn't add up

edit: I guess I should provide a more direct rebuttal. What I'm saying is, you've talked about the tech/PR side of this theoretical food delivery startup, but you've forgotten the food supply chain. That is actually a lot harder than the tech/PR side. It would require a highly substantial investment and fully custom logistics.