There are. FreshDirect has a state-of-the-art facility in the Bronx, and I'm sure Amazon has several ghost groceries also -- e.g. they just bought two Fairways locations.
Check out this video of the FreshDirect facility, it's actually pretty amazing: https://www.youtube.com/watch?v=fnIrwrCq_4Q
Instacart and the local grocery store should be able to work together to make incremental changes to what they are doing today. That seems like the low hanging fruit that could be put into operation in short order.
Also, back then the technology for sub-minimum-wage delivery gig workers hadn't been perfected yet.
I put in an order later in the day, and half the stuff I ordered was unavailable because the store shelves weren't being restocked before closing. I was stunned. I had naively assumed that the food was coming from an Amazon-like warehouse, where they knew exactly what was in stock prior to ordering. A pretty terrible experience overall.
I expect Amazon will at some point leverage Whole Foods to build a proper food warehouse with the experience we've come to expect from Amazon Prime. The big supermarket chains better get their act together quick, before Amazon eats their lunch.
They do this depending on your metro/area. Here in SF-proper (dogpatch) there is a brick and mortar Whole Foods ~0.7 miles away, but my Whole Foods online orders get packaged from a nearby Amazon Warehouse even closer to my residence.
The experience has been very good for me so far and I have no need for an Instacart-like service.
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.
It's worth noting that off the back of Ocado's success, all major UK supermarkets also offer online delivery. And my understanding is that this is mostly serviced directly from stockrooms rather than going via store shelves (albeit individual store stockrooms).
Around the same time Tesco (I can't find exact dates, but when I started working there in 2004 it had already been around for a while) launched their competing service, however they did so across the whole country (at any store big enough and with enough parking space to support it).
Ocado is building a business like Amazon warehouses, where they build warehouses and use their infra to provide fulfilment for other vendors.
If it isn't apparent by now, the people who are still walking around a large store aren't driven by efficiency. They want something to do / enjoy the routine of it, and don't want someone else picking out their stuff for them.
Just have warehouses/stores optimized for delivery and batch the orders. Boost productivity and start paying people decent already.