1. They're local. Most people have a grocery store within 5 minutes of their house.
2. They're well-stocked. You have ten thousand products to choose from. Who could ask for more?
3. They're timely. If you go to a grocery store, it will take you a certain maximum amount of time - the amount of time it takes to go down each aisle once.
4. They're accurate. You picked every item. Your fruit fits your exact criteria.
With grocery delivery, you can be perfectly local, but your stock is identical and your accuracy is almost always worse. And your time window + the time it takes to pick the two dozen items you need will almost always be worse than going to the grocery store.
That said, there is a niche for this - the elderly and the very, very busy. To capture the second niche, you'll need to up your timeliness though and improve your branding on speed. It should take no longer to deliver groceries than it does to deliver a pizza.
I want my DiGiorno delivered.