Best part is the convenience: We've set it up to deliver once a week, and so every week the day after the previous delivery they create a new order and we can edit it in their app or on their website, and optionally you can set it to auto-populate your order based on your shopping history, and they get it "close enough" that often we don't bother even checking the order (this week, for example, I didn't) and we know we'll get something that's "close enough" that worst case we'll pick up the odd thing extra when we're out anyway sometime during the week.
They deliver within the same 1 hour slot every week (unless we change it; if we do, they will show us when they have a car in the area if we want to try to be more eco-friendly, but won't put any restrictions on us if they have capacity), and it's very rare or them to miss it - when they do, the driver will call and explain why and give us updates. If they're able to deliver early, they'll call and ask, and if necessary (if we're out etc.) they'll do other deliveries first if they can or worst case sit and wait to deliver within the agreed time slot.
They'll carry everything into your kitchen if you wish, or wherever you want them to, and everything comes in colour-coded bags for freezer, fridge, and cabinets. The receipt list everything by minimum guaranteed use-by dates.
The precision in delivery makes all the difference. I rarely go into grocery stores any more, and I don't miss it.
I live in the 'burbs and I drive every day anyway. To me, the pain isn't the driving (though for some urban areas I'm sure it is), it's just the hassle of parking and shopping in a crowded, inefficient store (wasting my time), and hauling all my stuff back to the car.
I think theres a deeper psychological issue at play here too: delivered to your door makes you passive, at the "mercy" or whim of the company/person making the delivery. There's a subconscious anxiety associated with waiting in anticipation. Whereas, going out and picking up makes you the active one. Sure the store could make you wait, but if they design their system properly, "ready for pickup" should mean just that. But "out for delivery" could me 5m or 3 hours from now.