What if there was a mobile(not cellphone) grocer that frequented locations where people might consider buying from the grocer?
A grocer truck (like a food truck) could frequent train station parking lots as designated times allowing commuters to shop a couple of days' groceries. A grocer truck could frequent central locations in a neighborhood at designated times to allow residents to walk up to the truck to purchase groceries.
Upsides:
grocery when you need it without trips to the supermarkets
purchase less but more often than a once a week trip.
convenient location and timing to do grocery shopping
no parking hassles if the model is a walk up to purchase groceries.
downsides: limited choice (can be mitigated if grocer has a mobile app)
limited supply (again if there is an app and you can preorder the items are kept aside for you for a limited time before being sold) Perishable items cannot be set aside indefinitely.
limited pick up options (grocer can field location requests and can add a location if there is enough demand for it)
All this might have already been tried but I don't know of it. What other downsides do you see apart from the fact that some people would rather order from a restaurant than cook? This would not be for those people who don't want to cook.