In Canada take out places are adding grocery boxes, wine and beer to their take out menu's. Seems like this may not even need to involve grocery stores. Why not get some essentials if you are already getting delivery.
In my opinion, every solution that uses existing infrastructure and services is a good one. Because time is the main issue.
One big difference between this crisis and past catastrophes, which a lot of organizations are well prepared to handle, is, that noye all infrastructure is intact. Processes and supply chains are disrupted on a global scale, so.
Comparing that to, say, the tsunami catastrophes. In these cases, infrastructure was destroyed locally or, at the worst case, regional. The challenge was to build ad-hoc infrastructure to get stuff out of the global supply chains to the region. This approach doesn't work now.
I like the idea if piggybacking on food delivery services. There should be at least one in every village, or at least near by. It could run decentralized. And the principal would scale pretty well.