For groceries you have the additional challenge that different items need to be stored differently (cooled, frozen) during the time between getting retrieved from the big warehouse and being sent on their last mile.
You can build something for this, of course, but that’s expensive. In the case of Amazon, however, they already have facilities for storing smaller amounts of different groceries products that are relatively efficient for sending small amounts of products on their way for last mile delivery: they own supermarkets.
A decade ago I worked on some retail logistics and we ran up against exactly this problem. The solution we came up with was also exactly this: send workers into the nearest supermarket to collect the requested items from there. If you already own the supermarkets and have staff running around there, it’s a no-brainer. In fact, if you look closely you’ll see many retail companies, both large and small, do this.
Rather then supermarket employees running around the shop they build automated warehouses specifically optimised for picking/packing efficiency.
I simply don't see the reason for services like Instacart and Amazon fresh to exist... I can already get deliveries picked and dispatched by the super markets themselves. I count 6 different services within 5 miles of my home/office/isolation bunker.