Another possibility: For perishable goods in the sort of SKU counts typically offered, it can't work unless it has a certain minimum scale. Local supermarkets supported by a largely automated (and has been for 30 years) regional distribution center have that scale from walk-in traffic. A new delivery service using high-density storage could save on real estate and labor costs on the backend, but it has to have runway to replace a lot of the local market (which may take a decade), and the whole time you're scaling, these low-velocity SKUs are literally spoiling while these expensive, high-throughput robots are mostly idle. The frontend costs of delivery are a separate category of problem.

Replacing the regional distribution center instead with even higher levels of automation, and getting your groceries delivered from the same warehouse the supermarket is, would give you the scale from the start... but then that increases your frontend delivery costs and more importantly your frontend delivery latency; High latency is a much worse thing with milk than with books or hammers.