Why is a real fulfilment centre better? I can see an Amazon centre with robots etc being more efficient, but other warehouses seem no more efficient than going through shelves at a walmart.
For grocery fulfillment, I don't think they are better at scale. Because they are for from the customers, they are not everywhere. Existing stores, so, are there. They use established replenishment from existing warehouses. Which means you have to use existing staff and store processes (and software) to fulfill orders. Which is hard. So it's either expensive or hard to do (which could expensive in itself). Over simplified.
Warehouse trumps Supermarket for efficiency by multiple factors easy.
Just as an example imagine the 50 most ordered items. I can put these in a tiny area closest to my packers in a warehouse. How far to you think you'd need to push a cart between those 50 points in an average Walmart?
The semi-automated ones have different issues. Only Amazon really has the tech fully figured out to a degree where issues are resolved almost instantly. Amazon can also use less but larger scale fulfillment centers because they deliver mostly small objects at an arbitrary time, whereas you can't leave 6 bags of groceries at a front door.