This does not compute. They already have ship-to-store, and have had for quite a while. It hasn't made a significant impact on their online power. Customers don't want to drive to a Walmart to pickup their online order. That's an extra step for no reason.
I actually use the Home Depot site-to-store equivalent much more than the Wal-Mart one [probably several times a month, vs. once or twice a year]. Home Depot gets it right. There are still occasional problems, and it would be better if they could fulfill the orders faster, but it still avoids having to search for stuff, which I consider to be of significant value.
For driving it really depends on the city and the persons situation. Many people drive by a walmart on their commute, the ability to order something in the morning then pick it up on the way home would be convenient. For businesses someone could order something the night before and pick it up in the morning and use it at work that day, that would be very valuable.
Plus, Amazon lockers.
Nobody really has Amazon's physical goods delivery infrastructure. You can look at Wal-Mart and Target, but they have infrastructure designed to solve a very different problem, getting large amounts of the same goods to certain physical stores. They rely on semi-truck drivers to deliver palettes of goods to stores. What they don't have, for example, is Amazon's very close relationships to UPS and USPS. Could they develop it? Maybe. At great expense. Would they be able to peel off more existing Amazon customers than they'd be cannibalizing their own current sales? Who knows.