The typical grocery delivery service also has the luxury of batching orders (controlling cost) and delivers with refrigerated vehicles (consistent product)...seems more sustainable to me...but what do I know - to me, the Uberization of most markets (other than ride sharing) never seems to have a clear win on cost/benefit...
Also important for cost: An online supermarket can save a ton on rent by having fewer, much bigger fulfilment centres, located in cheaper slightly out of the way industrial zones. Classic supermarkets are generally in commercially attractive areas, close to traffic hubs or in downtown locations.
This is massive in the UK. Ocado run nothing but heavily automated warehouses as their online only, and a lot of the big supermarkets are starting to run similar locations optimised for delivery packing. Somewhat tangentially I've even heard of a couple of restaurant chains opening dark stores which do nothing but fulfil delivery orders.
I kind of question how much additional margin the average person will tolerate though. Will the same mom that spends time clipping coupons (or printing them) be willing to pay what it takes to make this worthwhile for Walmart? That's the demographic you want to entice if you want to make grocery delivery successful, not Johnny Ramen College kid.